re Properties of Sodium - DTIC · The nine PVT experiments for sodium (Table 2) covered a wide...

re Properties of Sodium

J P. TON • 'T. EWING, J. . PAN I

I. W. TDNKULUa, • D. WILLIAM , A.ND R. R. MrLL£Jt

September 24

U NA .. RESEARCH LABORATORY W ·~D.C.

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CONTENTS

Abstract ill Problem Status iii Authorization iii

INTRODUCTION 1

EXPERIMENTAL MATERIALS AND METHODS COMMON TO ALL MEASUREMENTS 1

EXPERIMENTAL MEASUREMENTS 2

Pressure-Volume-Temperature Measurements of Sodium 2 Density Measurements of Liquid Sodium 9 Specific He.'* Measurements of Liquid Sodium - 12

SUMMARY OF FUNDAMENTAL PROPERTIES USED IN THE THERMODYNAMIC TREATMENTS 14

Density of Liquid Sodium 14 Enthalpy and Entropy of Monomeric Sodium Vapor 14 Specific Heat at Constant Pressure of Monomeric

Sodium Vapor 14 Enthalpy and Entropy of Liquid Sodium 14 Saturation Pressure of Liquid Sodium 15 Enthalpy and Entropy of Vaporization of Sodium 15

THERMODYNAMIC TREATMENT OF PVT AND ASSOCIATED PROPERTIES 15

Virial Coefficients of Sodium 16 The Virial Equation of State uf Sodium 18 Thermodynamic Properties of Sodium by the Virial

Method (Monomeric Gas Path) 18 Thermodynamic Properties of Sodium by the Virial

Method (Liquid Path) 20 A Comparison of the Monomeric Gas Path and the

Liquid Path for Thermodynamic Calculations 21 Molecular Reactions in Sodium Vapor and Their

Equilibrium Constants 23 The Quasi-Chemical Equation of State of Sodium 26 Compositional Properties of Sodium by the

Quasi-Chemical Metnod 26 Thermodynamic Properties of Sodium by the

Quasi-Chemical Method (Monomeric Gas Path) 27 A Comparison of the Thermodynamic Properties by the

Virial and the Quasi-Chemical Methods (Monomeric Gas Path) 28

DISCUSSION OF QUASI-CHEMICAL TREATMENT AND COMPOSITIONAL INFORMATION 31

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CONTENTS (Continued)

DISCUSSION OF THERMODYNAMIC AND ENGINEERING PROPERTIES OF SODIUM

ACKNOWLEDGMENTS

NOMENCLATURE AND UNITS

REFERENCES

APPENDIX A - Saturation Properties of Sodium (Monomeric Gas Base)

APPENDIX B - Thermodynamic Properties of Sodium Vapor (Monomeric Gas Base)

APPENDIX C - The Molecular Composition of Saturated Sodium Vapor and Enthalpies of Vaporization

APPENDIX D - Molecular Composition of Sodium Vapor

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Sills Building. 5285 POM Knv.ii Road S|iiirixfit-lfl, Virginia 22151

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ABSTRACT

An experimental program is in progress at this Laboratory to measure various thermophysical properties of sodium, potassium, and cesium. A final reporting of the experimental results for sodium (saturation and superheat properties of the vapor, density and specific heat of the liquid) is presented together with a thermodynamic treatment of the data. Two equations of state are advanced, one virial and one quasi-cheir.ical; and additional saturation and superheat properties of the vapor are derived from these equations. Either of two paths can be used to compute thermodynamic properties, the monomeric gas path or the liquid path; but results obtained by the former procedure are believed to be more accurate. Enthalpy, entropy, specific volume, specific heat, and compositional information (weight fraction of dimer, weight fraction of tetramer,and average molecular weight) are tabulated for some 700 selected vapor states in the temperature range from 1625° to 2575°F and in the pressure range from 0.2 to 25 atm.

PROBLEM STATUS

This is a final report on the experimental work with sodium.

AUTHORIZATION

NRL Problem C05-15 NASA Contract Number NASA C-76320

Manuscript submitted Dacember 24, 1964.

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HIGH-TEMPERATURE PROPERTIES OF SODIUM

INTRODUCTION

In the development of compact turboelectric systems for space vehicles, the National Aeronautics and Space Administration is sponsoring a property measurement program for the evaluation of several liquid metals as possible working fluids. As an integral part of this program, the U.S. Naval Research Laboratory has measured several thermophysical properties of potassium to 2300° F, sodium to 2500° F, and cesium to 2300° F.

The saturated liquid properties which have been determined experimentally include density, vapor pressure, and specific heat (except for cesium). Saturated and superheated vapor properties including specific volume, specific heat, enthalpy, and entropy have been derived from experimental pressure-volume-temperature (PVT) studies. All phases of this measurement program have been completed. The final properties of potassium and cesium are published in companion reports (1), and those of sodium are presented in this report.

EXPERIMENTAL MATERIALS AND METHODS COMMON TO ALL MEASUREMENTS

A number of materials, methods, and techniques were common to many of the experimental measurements. These include the container alloy, the high-pressure furnace systems, the temperature measurements, and techniques for purifying and transferring the alkali metals. All are discussed at some length in the companion report on potassium (la), and only a short section related to the purity of the sodium will be included in this report.

Sodium samples for the density and specific heat detrvminations were distilled directly from a small nickel still (2) into each apparatus. However, for the PVT determinations this procedure was impractical, and the alkali metal was distilled and introduced into small capsules (la) for subsequent transfer into the PVT apparatuses. Sodium introduced to the distillation retort was a pure grade of E. L du Pont de Nemours and Company; a typical spectrographic analysis after one distillation at this Laboratory is presented in Table 1. It will be noted that metal impurities are present in very low concentrations.

Sodium oxides, which may be present in low concentrations in the distilled metal, should be effectively gettered by the columbium and zirconium of the container alloy. Therefore, oxygen analyses of the metal samples used in these studies were not made, but the oxygen content of sodium (as purified in previous studies (3) at this Laboratory by the same distillation technique) was determined to be below 10 ppm by the amalgama- tion method.

Table 1 spectrographic Analysis of Distilled Sodium

Metal Analyses (Parts per Million by Weight)

K 1 to 100 Rb Not Detected Cs Not Detected Li Not Detected

2 NAVAL RESEARCH LABORATORY

EXPERIMENTAL MEASUREMENTS

Pressure-Volume-Temperature Measurements of Sodium

Experimental Superheat Results - The PVT measurements in both the superheat and saturation regions were made with small closed chambers using flexible diaphragms as null-detectors. This high-temperature columbium-1% zirconium apparatus and the methods employed are described in detail for potassium (la); thus, only the new experimental results for sodium are included in (his report.

The nine PVT experiments for sodium (Table 2) covered a wide range in the superheat region with measured temperatures extending from 1760° to 2590° F and pressures from 1.9 to 25.1 atm. For each experimental point in this table, pressure and temperature were directly observed and the specific volume was computed from the weight of sodium added to the chamber. The inconsistent numbering cf the sodium experiments may be misleading; it results from these experiments being performed concurrently with those for potassium and cesium.

At each equilibrium point represented by the data in Table 2, multiple readings of temperature and pressure were made at 5 to 10 min intervals until successive readings showed a temperature drift of 0.07oF/min or less and a temperature difference across the chamber less than 20F (and generally less than 10F). In the measurement of pressures with the diaphragm device, the excellent reproducibility obtained during the potassium measurements (la) continued for sodium. Measurements for each experiment (except experiment 18) were made over a minimum of one full cycle from the normal boiling point to about 2525° F, and equilibrium pressures were reproduced in the superheat region to better than ±0.1 psi before, during, and after cycling.

Specific Volumes of Saturated Vapor - Specific volumes* of several saturated vapor states (Table 3) were observed over the temperature range from 1750° to 2555° F. The measurements were made in the course of the PVT studies, and each point represents an intersection of the saturated and superheated vapor curves for one of the nine PVT experiments. However, for the low-weight and low-pressure experiments (particularly 3, 4, 18, and 19), the observed pressures near the intersection of the saturation and superheat curves were found to be abnormally low. To study this phenomenon, a large number of observed points were taken in this region for experiment 3, and a portion of this experimental curve is presented as Fig. 1. It will be noted that for a temperature range of about 150°F observed pressures are significantly below the true saturation and superheat curves. The several factors which may contribute to this lowering phenomenon include the existence of dual states, elevation of the boiling point by nonvolatile impurities, and the retention of condensed alkali metal on the walls by adsorption and capillarity effects. These factors are discussed in some detail in Ref. la.

The saturated specific volume for each PVT experiment was obtained, as illustrated for experiment 3 in Fig. 1, by a short extrapolation of the superheated vapor curve to the true saturation curve as defined by the vapor-pressure equation (Eq. (1)). Although the extrapolation procedure l nded to minimize any error in the saturated specific volume resulting from the depression phenomenon, it is believed that specific volumes obtained from the virial equation (Eq. (14)) and the vapor-pressure equation (Eq. (1)) will be of higher reliability than those observed at the intersection points (Table 3). Even so, corresponding values computed from the virial equation show an average deviation of only ±0.57% from the observed values.

*Preliminary values for the specific volume of saturated sodium vapor (29) were based on incorrect therma1 expansion values for columbium-1% zirconium.

NAVAL RESEARCH LABORATORY

Table 2 Pressure-Volume-Temperature Measurements . Superheat Region

Temperature (0F)

Pressure (abs atm)

Specific Volume (cu ft/lb)

Temperature TF)

Pressure (abs atm)

Specific Volume (cu ft/lb)

Experiment 3 Experiment 20

21?6.7 2231.4 2324.3 2414.3 2508.6 2472.8 2376.9 2287,8 2185.9 2113.3 2095.5 2099.3 2102.9

6.623 7.033 7.375 7.701 8.025 7.909 7.568 7.236 6.860 6.579 6.478 6.497 6.514

10.750 10.767 10.783 10.798 10.814 10.808 10.792 10.777 10.760 10.748 10.745 10.746 10.746

2317.9 2382.2 2449.4 2514.0 2486.4 2419.5 2353.8 2284.2 2238.1 2204.6

9.709 10.027 10.368 10.677 10.549 10.216 9.886 9.536 9.304 9.123

7.8521 7.8600 7.8684 7.8766 7.8731 7.8646 7.8565 7.8479 7.8424 7.8383

1 Experiment 23

2399.9 2517.3 2536.1 2491.4 2456.3 2417.4 2373.2 2341.9 2306.2

13.250 14.053 14.175 13.884 13.628 13.367 13.078 12.860 12.547

5.8001 5.8110 5.8128 5.8086 5.8053 5.8017 5.7977 5.7948 5.7916

Experiment 4

1807.3 1959.8 2110.5 2333.5 2445.5 2537.2 2397.9 2258.1 2157.4 2059.3 2019.4 18S!.2 1825.2 1767.4 1758.2

1.9237 2.1162 2.2999 2.5442 2.6613 2.7552 2.6089 2.4605 2.3510 2.2394 2.1931 2.0427 1.9604 1.8849 1.8631

33.399 33.472 33.547 33.662 33.722 33.772 33.697 33.623 33.571 33.522 33.502 33.439 33.407 33.380 33.375

Experiment 7

2571.6 2572.3 2576.5 2579.0 2581.9 2582.6 2586.4 2588.0 2579.9

24.837 24.850 24.935 24.983 25.044 25.054 25.123 25.146 25.014

3.0693 3.0693 3.0695 3.0696 3.0698 3.0698 3.0700 3.0701 3.0697

Experiment 18

2051.1 2172.0 2273.6 2387.1 2521.8 2479.6

4.992 5.326 5.612 5.921 6.268 6.162

13.920 13.945 13.967 13.992 14.022 14.012

i

Experiment 25

2439.5 2479.2 2524.5 2511.9 2491.8 2468.2 2452.1 2433.5

17.259 17.632 18.020 17.917 17.745 17.540 17.403 17.209

4.3766 4.3794 4.3826 4.3817 4.3803 4.3786 4.3775 4.3762

Experiment 19

1971.9 2099.4 2193.0 2306.9 2417.5 2520.7 2472.4 2373.2 2248.6 2141.7 2038.8 1942.4 1910.2

3.4737 3.7241 3.9194 4.1270 4.3161 4.4985 4.4121 4.2474 4.0269 3.8174 3.6023 3.4145 3.3472

19.759 19.796 19.824 19.859 19.894 19.927 19.911 19.880 19.841 19.809 19.778 19.750 19.741 L

Experiment 17

2534.4 2516.1 2506.6 2502.7 2496.6 2495.7 2490.5

21.023 20.832 20.723 20.676 20.604 20.589 20.506

3.6747 3.6736 3.6730 3.6728 3.6724 3.6724 3.6721


Table 3 Specific Volumes of Saturated Sodium Vapor

Experiment j Number

Temperature (0F)

Specific Volume 1 (cu ft/lb)

4 ^SO.l 33.37 |

19 1888.3 19.73 j

18 1988.8 13.90 |

3 2071.8 10.74

20 2177.6 7.835 i

23 2289.0 5.790

| 25 2402.3 4.374

17 2474.4 3.671

7 2555.1 3.069

TRUE SATURATION CURVE

OBSERVED SUPERHEAT CURVE

OBSERVED SATURATION CURVE

IB 19 20 21 22 23 24 25

t ■ 10'CF) «..c

Fig. 1 - Phenomenon at intersection of saturation and superheat curves (illustrated with experiment 3)

f

NAVAL RESEARCH LABORATORY 5

Discussion of Superheat Results - The sources and magnitudes of errors in the PVT measurements were discussed in detail for potassium (la). Many of these are common to the PVT studies of all the alkali metals, and only those which are specific to the sodium work are included here.

Although the procedures developed with potassium for the degassing and closing of null-point apparatuses were very effective in excluding all inert gas from the chambers, the possibility of inadvertently trapping gas in a chamber still existed. Therefore, each sodium apparatus was checked for gas at the conclusion of an experiment by opening the chamber to an evacuated manometer. Gas pressures as low as 0.01 psi were detectable in this manner, and no gas was detected in any of the nine experiments for sodium.

Two apparatuses of significantly different surface-to-volume ratios were used in the potassium study (la). A comparison of compressibility factors measured with the two apparatuses provided evidence that any adsorption of potassium on the metal surfaces was insignificant. For sodium, two experiments (18 and 19) were again made with a large apparatus of nominal 113 cc volume and a surface-to-volume ratio of 1.64 cm"x. The remaining experiments were made with the standard 57-cc apparatus having a surface-to- volume ratio of 2.15 cm"1. If adsorption of sodium had been significant, one would expect the low-weight experiments performed with the lower surface-to-volume chambers to have observed pressures which would appear high relative to the other experiments. The fact that the observed pressures for these two experiments are not high provides additional evidence that any surface adsorption was insignificant.

The factor of thermal ionization was discussed for f ntassium vapor in Ref. la. An estimate of the degree of ionization was obtained for sodium from its ionization potential (4). For the metal vapor at 2500°F and 1 atm, the degree of ionization was estimated to be less than 10"7. This calculation leads to the conclusion that the degree of thermal ionization is several orders of magnitude too low to produce a measurable increase in pressure.

The results of PVT measurements are generally reported in the form of compressibility factors (pV/RT), since these factors, in one form or another, are employed directly in the thermodynamic reduction of data. It ie then desirable to express experimental error in terms of these factors. If we take into account all known sources of uncertainty, the percent probable error in the compressibility factor ranges from a minimum of 0.26% to a maximum of 0.44%. The relatively large error occurred in experiment 4 and was generated by uncertainty in the weight of the very small sample of sodium employed.

Experimental Saturation Pressures - Saturation pressures of sodium for the full temperature range (0.34 atm at 14370Fto 23.8 atm at 2539°F) were measured with a separate PVT apparatus using a large excess of the alkali metal, and the results are presented in the "Vapor-Pressure Experiments" section of Table 4. Pressures to 12.9 atm which were measured in the course of eight PVT experiments are presented in the second section of the same table. It has been shown that saturation pressures observed for each experiment near the intersection of the saturation and superheat curves were below corresponding values on the true saturation curve. This lowering of the vapor pressure can be satisfactorily explained (la), and observed pressures in these regions are not included in the table.

The vjyjor-pressure data in Table 4 are presented graphically in Fig. 2. It is evident from a large-scale plot that log p versus IT for sodium is not linear, but the data can be effectively fitted for the full temperature range (normal boiling point to 2^40oF) with one three-term equation of the Kirchhoff type (log p =or + 6/r + c log T). Afew measurements of vapor pressure below 1 atm are included in Table 4 and Fig. 2, but these are believed to be of lower precision and were given no weight in determining the coefficients of the vapor-pressure equation.


Table 4 Saturated Vapor Pressures of Sodium

Temperature Pressure Temperature Pressure (0F) (abs atm) (0F) (abs atm)

Vapor-Pressure Experiments

1693.3 1.4283 2304.8 13.077 1800.7 2.3197 2223.9 10.363 1910.1 3.587 2152.5 8.329 2009.2 5.172 2053.0 6.023 2116.7 7.442 1947.0 4.131 2183.3 9.155 1837.3 2.7035 2262.4 11.582 1722.1 1.6399 2331.4 14.063 1628.1 1.0472 2413.1 17.466 1593.6 0.8737 2470.1 20.164 1557.7 0.7172 2539.2 23.821 1513.1 0.5512 2511.6 22.297 1478.7 0.4464 2443.4 18.851 1437.0 0.3362 2381.1 16.065

Vapor Pressures from PVT Experiments

1690.0 1.4242 1769.2 2.0325 1640.5 1.1187 1851.4 2.8729 1772.4 2.0645 1947.4 4.113 1872.0 3.1138 1810.4 2.4081 1976.7 4.607 1661.5 1.2391 2075.5 6.505 1692.9 1.4249 2189.7 9.347 1635.8 1.08C7 2299.8 12.916 1709.2 1.5365 2149.2 8.237 1651.5 1.1697 2017.0 5.318 1634.4 1.0744 1906.7 3.562 1645.5 1.1500 1738.4 1.7835 1758.2 1.9291 1636.9 1.1085 1854.1 2.8933 1688.4 1.4017 1958.9 4.301 1633.4 1.0772 2062.0 6.212 1695.8 1.4630 2168.6 8.764 1825.3 2.5681 2135.3 7.831 1760.5 1.9522 2020.6 5.348 1696.9 1.4671 J905.0 3.506 1629.1 1.0629 1716.4 1.601 1636.9 1.0860 1765.5 1.9700 1863.9 2.9831 1873.6 3.1056 1810.4 2.4102 1988.7 4.799 1678.0 1.3371 1937.6 3.994 1648.4 1.1622 1813.7 2.4442 1779.6 2.1366 1700.7 1.4820 1880.6 3.2288 1623.7 1.0221 1998.7 4.986 1639.2 1.0853 1937.0 3.996 1760.3 1.9223 1728.4 1.7052


1 2 - %.

1 0 - So.

08 - Hj.

06 - Vi

04 - \

02 \.

00 \.

02 - N. 04

n R 1 1 1 1 1 -

1 i I i l 1 32 34 36 38 40 42 44 46 48 SO

IOVT

52 54

Fig. 2 - Vapor pressure of sodium as a function of the reciprocal absolute temperature

Three vapor-pressure equations

9.980.94 loB p 6.83770 - - 0.01344 log 7'

log p = 7. 11285 - 10, "63- 7 - 0.68464 log T

(1)

(2)

loj? p - 7.00980 10. 035. 2 0. 65769 1 o« T (3)

for sodium were obtained by least-squares (computer) treatments of the data. Eq. (1) was derived from a treatment using all the observed vapor pressures above the normal boiling point. Eq. (2) was derived from twenty points selected at equal intervals of i T from a smoothed plot of log p versus 1/T for all the data. Eq. (3) was derived from the data of the vapor-pressure experiments in the first section of Table 4. The average deviation of all the observed vapor-pressure data in Table 4 from corresponding values computed from any one of the three equations is iO.37%. The three equations are, therefore, effectively equivalent, but other thermodynamic quantities in this report are based on Eq. (1). The normal boiling point as obtained from Eq. (1) is 1618.6°F (881.40C) and from Eqs. (2) and (3) is 1619.0oF(881.7oC).

The NRL vapor pressures are compared to those of previous investigators in Fig. 3. Vapor pressures of sodium above the normal boiling joint have been observed by Bowles and Rosenblum (5) over the temperature range from 1778° to 3418°F, by Sowa (6) over

NAVAL ftESEAIKH LABORATORY

14

12

10

a

6

4

2

0

-2

4

6

8

-10

-12

1

-" j

^ ^ BOWLES AND ROSENBLUM _

^ ^ ^-■^

N MAKANSI NRL

> y ^

■

■

■^

KIRILOV AND GRACHEV^_^--^^^ 1

■

1 1 'l 1 1 1 1 1 1 1 1 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000

TEMPERATURE CR)

Fig. 3 - Comparison of vapor pressure data of sodium by several investigators using the NRL. data as standard

the range from 1652° to 2534° F, by Kirilov and Grachev (7) over the range from 1616° to 2372° F, and by Makansi et al. (8) over the range from 1146° to 2075°F. In Fig. 3 the NRL results have been arbitrarily taken as standard, and the percent deviation of the vapor pressure of each investigator from that of NRL is plotted as a function of temperature. It will be noted that the vapor pressures observed by Makansi are in excellent agreement and those by Bowles and Rosenblum in good agreement with the NRL data. The data by Sowa exhibit a positive deviation at higher temperatures which apparently is outside the range of combined experimental errors. Kirilov and Grachev have reported results for both potassium (9) and sodium (7), and the data for each metal deviate widely from all published work.

As an independent check c the internal consistency of the vapor-pressure measurements, the heat of vaporization to the monomer at absolute zero was computed for each observed saturation point with the relationship

^Oo) = -ff — + + r \n n - In £—

2 V ;l V HT

♦ 2.201997' - 0.399185r log 7' + 0.552615> 10'*7"

0.056682* lO-7?"3 - 12,172 (.-«Mao/T-. 29.023 (4)

This working equation was derived from the third law as described for potassium (la). The computed vaporization heats (converted to cgs units) are plotted as a function of temperature in Fig. 4. Theoretically, the same value of ( \^),, should be obtained for all the saturation points, and there is reasonable constancy. The small temperature trend of ( \A^)(i can result from errors in the vapor pressure, the virial coefficients, or in any of the free-energy functions employed in the computations. The free-energy functions of the liquid appear to be the least reliable quantities. These functions are known precisely


25.7

i P <

§ 25.6

_i <

> o o I o 25.5

25.4

9

"Oft, O 0 0 0

'" o %,

1400 1600 1800 2000 2200 TEMPERATURE CF)

2400 2600

Fig. 4 - Heat of vaporizr.tion of monomeric sodium at absolute zero as computed from observed vapor-pressure data

only to 1650° F and above this temperature must be obtained by an extrapolation of the liquid specific-heat results of Ginnings (see "Specific Heat" section). This extrapolation was roughly justified to 2100° F by a few specific-heat measurements made at this Labora- tory, but it is believed that the true vaporization heat (25.61 kcal/mole) may be obtained from saturation data below 1700° F and that the temperature trend above this point results from error in extrapolating the specific heat of the liquid.

Piscussion of Saturation Pressures - The measurement of saturation pressures directly with a diaphragm detector is new to the high-temperature field. The relative merits of the apparatus and the uncertainties to be expected ir the various measurement parameters are discussed in the potassium report (la). If «._ take into account all known sources of error in the saturation measurements, the percent probable error in the pressure ranges from ±0.64T at 1 atm to a maximum of ±0.80^ at 23 atm.

Makansi (8) has measured vapor pressures of a number of the alkali metals including sodium and potassium by the boiling-point method. The NRL results for both potassium and sodium by a static method are in close agreement with the corresponding results of Makansi. This fact tendß to increase the degree of confidence which can be placed in the observed saturation pressures for both metals.

Density Measurements of Liquid Sodium

The density^ of liquid sodium was determined with columbium-l^ zirconium pyenom- eters of 30 cc nominal volume by the method described for potassium (la). Measured densities over the temperature range from 1577° to 2491° F are reported in Table 5 and presented graphically along with those of other investigators in Fig. 5. The recommended

^Preliminary values and equations for the density of sodium (29) were based on incorrect values for the thermal expansion of columbium-1% zirconium.


Table 5 Density of Liquid Sodium

at High Temperatures

Temperature (0F)

Density (Ib/cu ft)

1576.8 46.738

1886.2 43.926

2093.5 42.224

2268.9 40.641

2491.2 38.933

density equation for liquid sodium from the melting point to 2500° F is

dl =59.S66 - 7.9504x W3t • 0.2872 I0'6t2 + 0.060iSx wV . (5)

This equation was derived by fitting the best curve to the density determinations of Hagen (10) and NRL (11) at lower temperatures, Novikov et al. (12), Jackson et al. (13), Rinck (14), and Nishibayashi (15) at moderate temperatures, and NRL (Table 5) at higher temperatures. All these measurements are summarized in Table 6. For each investigation, the temperature range, the general method, and the average deviation from Eq. (5) are presented. In general, the dilatometric measurements show good internal consistency over the full temperature range, and it is believed that Eq. (5) will give density values which are accurate to ±0.3% between the melting point and 1100oF and to ±0.4% between 1100° and 2500°F.

Table 6 Summary of Density Measurements for Liquid Sodium

Investigator Method Temp, Range CF)

% Average Deviation [Obs.-Calc. (Eq. (5))1 L Calc.

NRL (11) Dilatometric mp to 503 ±0,08

Jackson (13) Buoyancy 937 to 1314 -0,74

Rinck (14) Buoyancy 804 to 1183 +0.15

Hagen (10) Dilatometric mp to 336 ±0.05

NRL (Table 5) Dilatometric (Pycnometers)

1577 to 2491 ±0.17

Novikov (A)* (12) (B)t

Buoyancy Buoyancy

248 to 505 275 to 1324

-0,14 +0,71

Nishibayashi (15) Buoyancy 486 to 1580 ±1.09

'''(A) with steel sinker. t(B) with tungsten sinker.

The uncertainties to be expected in the various parameters of the NRL density measurements were discussed in the potassium report (la). If all known uncertainties are taken into account, the percent probable error of the reported densities range from ±0.25 to ±0.30%.


(id fiD/ai) P


Specific-Heat Measurements of Liquid Sodium

Specific heats of saturated liquid sodium were determined from 212° to 2140° F. A bucket containing the alkali metal was equilibrated at a known temperature in a specially designed furnace and dropped into a copper-block calorimeter, permitting a measurement of the heat evolved in cooling the sample to 30° C. This procedure was repeated at a number of furnace temperatures for both filled and empty buckets, and the heat capacities of the sample were derived by standard calorimetric procedures. The specific-heat system and the methods employed have been described in detail by Walker et al. (17).

The heat capacities of sodium and of sapphire, a calorimetric standard, are presented in Tables 7 and 8. The observed values for each material are compared to corresponding values obtained at the National Bureau of Standards (18). Comparison results for sodium above 1650°F, the limit of the NBS measurements, represent an extrapolation using the NBS specific-heat equation. Although the deviations for each material are generally below ±3%, they are higher than those obtained in previous measurements with the same calorimetric system. The majv.r portion of this error stems from a large random uncertainty observed in duplicate measurements. During the potassium study (la), the method and the calorimetric system were completely re-examined 'or possible sources of error, but no significant source was discovered. It is now believed that the reduced measurement precision resulted from the relatively low sample-to-container heat-content ratio (1:3) which tended to magnify nominal system errors. It was necessary to use the thick-walled Inconel container, with its accompanying unfavorable heat-content ratio, in order to with- stand the pressure of potassium vapor at operating temperature.

Table 7 Specific Heat of Saturated Liquid Sodium (High-Ternperature System)

j Temp (0F)

NRL CP

(Btu/lb-0F)

NBS rP

(Btu/lb-0F)

Percent Deviation | fimLcp -NBS c\ \

\ NBSrp J

1111.1 0.301 0.300 +0.3

1335.0 0.291 o.äoi -3.3

1519.5 0.297 0.304 -2.3

1688.9 0.313 0.309* + 1.3

1848.0 0.324 0.316* +2.5

2029.3 0.325 0.326* 0.0

Mean ±1.6 i

«Extrapolated with NBS equation.

Specific heats of sodium at intermediate temperatures were measured at NRL several years ago but were not published. These results are now reported in Table 9 and compared with correp'^onding NBS values. The mean deviation of the data is only ±0.5%, because the measurements were made under more favorable conditions using an iron bucket with a sample-to-container heat-content ratio of 2:1.

The specific-heat results at both high and intermediate temperatures are presented graphically in Fig. 6 and are compared to the existing data and curve of Ginnings, Douglas, and Ball (18). The intermediate temperature results of NRL are in good agreement with those of NBS. The dashed curve above 1650° F represents a temperature extension of Ginning's data using his specific-heat equation. Although the higher temperature NRL


Table 8 Specific Heat of Sapphire (High-Temperature System)

NBS ! Temp (0F)

NRL C

P

(Btu/lb-0F)

533.8 0.246

1197.5 , 0.279

1334.1 0.285

1516.3 0.292

1682.8 0.292

1848.9 0.304

2034.3 0.303

(Btu/lb-0F)

0.250

0.286

0.292

0.296

0.298

0.301:c

0.303

Percent Deviation IRL - NBS c

NBS

-1.6

-2.4

-2.4

-1.4

-2.2

+ 1.2

0.0

Mean ±1.6 ^Extrapolated with NBS equation.

Table 9 Specific Heat of Saturated Liquid Sodium (Low-Temperature System)

NRL Temp (0F)

311.4

491.5

665.6

841.5

1031.5

1206.7

(Btu/lb-0F)

0.325

0.315

0.312

0.304

0.297

0.300

NBS C

P

Percent Deviation i ^NRL cp - NBS c^ I

(Btu/lb-0F) \ NBS ';. i 0.325 0.0

0.315 0.0

0.308 + 1.3

0.303 +0.3

0.300 -1.2

0.300 0.0

Mean ±0.5 . )

Ü.38r-

036

m

co

o.

034

0.32

030

0 28

026 J_ J 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

TEMPERATURE CF)

Fig. 6 - Specific heat of liquid sodium O NRL (low-temperature system) O NRL (high-tempe rature system)

14 NAV/L RESEARCH LABORATORY

results tend to verify an extension of the NBS equation to 2200°F, the true specific-heat curve for the liquid above 1650° F is in question.

SUMMARY OF FUNDAMENTAL PROPERTIES USED IN T'üE i HERMODYNAMIC TREATMENTS

Deuäiiy oi Liquid Sodium

Densities of the condensed phase were obtained from Eq. (5), which was derived from the observed data of this Laboratory and of other investigators.

Enthalpy and Entropy of Monomeric Sodium Vapor

Equations for absolute enthalpy and entropy of monomeric vapor as functions of temperature were derived from the work of Evans et al. (19) and are based on their standard enthalpies and entropies for the monomeric gas over the temperature range from 0° to 2800°F and on the enthalpy of vaporization at 0oR (26.10 mean kcal/mole) as obtained from the vapor-pressure data of this Laboratory. The equations for the monomeric gas at 1 atm (relative to the solid at 0oR) are

(hy)0 -- 2005.15 +0.21598 r+ 12. 172 «>• *'• 830/^ (6)

CsV = 0.23859 + 0.21598 in T. (7)

Specific Heat at Constant Pressure of Monomeric Sodium Vapor

The temperature equation for the specific heat of monomeric vapor at constant pressure was also derived from the work of Evans et al. (19) and is based on their computed specific heats over the temperature range from 0° to 3300° F. The relation for the monomeric gas at 1 atm is

{c*)0 =0.21598 +6.053 e-3T,280/f _ ^jj

Enthalpy and Entropy of Liquid Sodium

The thermodynamic properties presented in this report are based on the properties of the monomeric gas at 1 atm, but comparison calculations were made using the properties of the saturated liquid as a starting point. The absolute properties of the liquid (relative to the solid at 0oR) were computed with

h\ =0.389352 r- 0. 552955x10-T2 + 0. 113726'lO''Z'3 - 29.023 (9)

»j = 0.896497 log 7 - 1. 10557*10-4r + 0. 170408*10-'f2 - 1.792026 . (IQ)

These equations were derived directly from the work of Ginnings et al. (18) and are based on their specific-beat equations for the solid and liquid over the temperature range 32° to 1650° F. The absolute enthalpy and entropy of solid sodium at 32° F were taken from the work of Evans et al. (19). The specific heat of liquid sodium was also measured

NAVAL RESEARCH I ABORATORY 15

at this Laboratory (see "Specific Heat" section) for the temperature range from 600° to 2150° F. The NRL results overlap and extend the NBS range with an average deviation from their equation of only ±1.5%. Therefore, the upper measured limit of Eqs. (9) and (10) is extended to 2150°?, but thermodynamic cr'culations to 25750F with the liquid base still require a 400° F extrapolation of the specific-heat data.

Saturation Pressure of Liquid Sodium

Three vapor-pressure equations were derived from least-squares correlations, but Eq. (1) was selected to compute other thermodynamic quantities in this report.

Enthalpy and Entropy of Vaporization of Sodium

Heats of vaporization were calculated with

^« r 'P.. 22 982 t£lI2£ . 0.61344 («-/- <i) (11)

which was derived by a differentiation of Eq. (1) and a substitution into the Clapeyron equation. A value of »j at each temperature was obtained from Eq. (5) and a value of »f from the virial equation of state (Eq. (14)).

The entropy of vaporization at each saturation point was obtained by dividing the appropriate enthalpy change by the absolute temperature as shown in

A«,, - -~-' (12)

THERMODYNAMIC TREATMENT OF PVT AND ASSOCIATED PROPERTIES

The imperfections which occur in the alkali metal vapors and the various treatments of these imperfections in the reduction of PVT data are discussed at some length in the potassium report (la). A quasl-chemlcal analysis of the PVT data presented later in this report tends to identify the dimeric and tetrameric species, and it is believed that the major imperfection in sodium vapor stems from the existence of these higher- molecular-weight species. The species are present in sufficient abundance to require consideration of their presence In the determination of the thermodynamic properties of the vapor.

The important properties (enthalpy, entropy, and speeiüc heat) may be reduced from the PVT data by the use of either of two methods, the virial or the quasi-chemical. In the first, the gas is treated as a monatomic assembly with all apparent imperfections given by a virial equation of state, and the thermodynamic quantities are obtained as corrections to those of the monatomic gas in terms of the virial coefficients. In the second method, equilibrium constants are derived for the mobile equilibria by treating the gas as a mixture of molecular species, and other thermodynamic quantities are derived from the enthalpy changes associated with changes in the molecular composition of the vapor. For the latter method, it is assumed that all species behave as perfect gases.

The virial equation of state with coefficients through the fourth virial was reduced from the raw PVT data and used to compute enthalpies, entropies, specific volumes, and sperific heats for the vapor states of sodium. The alternative equation of state consistiu^ of the perfect gas equation and the equilibrium constants of the association reactions was


used as a check to compute the same engineering properties and, in addition, to compute the molecular composition for saturated and superheated vapor states. Since both of these methods were used in preliminary analyses of the compressibility data, the application of each method to the sodium iata will be described in some detail later in this report.

The thermodynamic properties of sodium by both the virial method and the quasi- chemical method were computed along constant temperature lines. The starting point for a particular property could have been the absolute value of that property for either the saturated liquid or for the monomeric gas at 1 atm. Therefore, two computational paths exist for obtaining each absolute property in the superheat region. The engineering properties were computed along both paths by the virial method, and the results are compared in this report.

Virial Coefficients of Sodium

The virial equation of state in the volume expansion form

pV , ß C I) /Fr = 1 + ^ + ^+p+ ••• (13)

was used for the analyses of all three alkali metal systems The virial coefficients for sodium in this equation were reduced from the PVT data by the method described for potassium (la). The coefficients are temperature dependent and were derived graphically by plotting functions along constant temperature lines. The small experimental errors in the PVT data were again largely systematic, which permitted the use of the adjustment procedure (la) to derive a more precise temperature coefficient for each virial.

The adjustment procedure required the selection of a reference isotherm with the maximum pressure range of compressibility factors in order to obtain the maximum definition of the virial coefficient. Accordingly, a reference temperature of 2525° F was selected. The compressibility factor * at this temperature was plotted as a function i/i^ (Fig. 7), and the second virial coefficient « was obtained as the lim dz/d{ i/v) as i/v - o^ Also,Ja - \)v was plotted as a function of i V and B was obtained as the lim (e ■ DV as i/F - o . The value of H by either procedure appeared to lie between 22 and 26, but 24.3 was selected, since this gave the best internal consistency between the low- and high-pressure results as determined from a plot of [(? - i)i* - H]V versus i v. From this final plot of the quantity [(a - \)v ■ n]v versus i/r , the adjustment factors were computed from the best linear curve drawn through the data (Fig. 8).

Assuming all errors to be systematic, the compressibility factors for each of the nine experimems were adjusted at all temperatures by the factors obtained at 2525° F. Using these adjusted compressibility factors, which are identified by .?* in all quantities, i z* - \)V was plotted as a function of \v for isotherms at 50-degree intervals between 2175° and 2575° F, and second virial coefficients were obtained from these plots. Third and fourth^virial coefficients were obtained by plotting the quantity [{B* ■ \)V - H] v versus 1 V for isotherms at 50-degree intervals between 2175° and 2575°F. Additional second virial coefficients in the lower temperature range from 1775° to 2125° F were obtained by computing the average value of [U - DK - cv ■ DV

2] tor the lower

pressure experiments on each isotherm. The values of C and I) required for these calculations were obtained by extrapolating their temperature equations. Virial coefficients are functions of equilibrium constants (la), and each coefficient can be represented for the full measured temperature range by a simple exponential relationship in 1 7 (Eq. (14)).

Experimental PVT data were also obtained from 2175° to 1775° F, but the number of experimental points in this region di^ not permit one to obtain reliable virial coefficients


1 00

\ X

0 96 — \

0 92 —

\ \SP

0 88 _

V* ^^Nv 0 84

\ ^ \

0 80 — \

076 — 1 1 1 1 1 1 1

12 14

Fig. 7 - Plot of ftV HT versus 1 V for sodium at 2525° F

1100

Fig. 8 - Plot of [{i • l)V - H] V versus 1 V for sodium at 2525° F (vertical line for each point represents probable error)


by the graphical method. Consequently, before the virial equation of state for sodium was acceptable for calculations below 2175° F, it was necessary to determine its fit to the observed lower temperature data. At temperatures and pressures corresponding to the observed low-temperature points, compressibility factors were calculated and compared to the observed values. The fit of the virial equation of state to the lower temperature data was found to be practically equivalent to that obtained at higher temperatures.

It should be emphasized that the procedure of adjusting the data (in no case did an adjustment factor exceed 0.7% of 2) was used only as an expedient in obtaining more precise temperature coefficients for the virials. Equally valid virial and temperature coefficients could have been obtained more laboriously from unadjusted data.

The Virial Equation of State of Sodium

The virial equation of state of sodium,:: with coefficients through the fourth virial ii

where

log I ß I - - t. :ir.iQ + ^i^ + log r

B < 0

(14)

log C -0.61:1: +

r > 0

10, 839

T

>g i D = -0. ()"'.. 13,539

T

I) < Q

The fit of the virial equation to measured data is shown graphically in Fig. 9, where compressibility isotherms generated with Eq. (14) are compared to experimental com- pressibilities at 100-degree intervals from 1775° to 2575° F. The observed specific- volume data in Table 2, or comoressibility factors derived from that data, may be calculated from the virial equation with an average deviation of 4 0.26^. As in the case of the potassium data (la), this deviation is of a magnitude predicted by random and systematic errors in the null-point measurements.

Thermodynamic Properties of Sodium by the Virial Method (Monomeric Gas Path)

Expressions for the thermodynamic properties (monomeric gas path) in terms of the second and thirH virial coefficients were derived by Hirschfelder et al. (20). By the same method, another set of equations was derived and extended to include the fourth virial

-The preliminary virial equation for sodium (29) was based on incorrect values for the thermal expansion of columbium-1% zirconium.


Fig. 9 - Compressibility of sodium vapor at several temperatures

500* F

coefficient. These equations were used to compute the thermodynamic properties of sodium vapor (Appendixes A and B) and are presented in this section.

Enthalpy, Entropy, and Specific Heat of Saturated and Siperheated Vapor - These properties at all vapor states were computed along isotherms using the following equations:

A fA-V HI 1 « i y L

T dJ. r .1 '!£ 2 \<iT ,. i 3 Ur

(15)

( * I ■ — I n f> . ,niLl . « , I /^ ( _L- , J_ A RT V V il 2V2 -IV1 \'n

dC I)

31 . 3 3V

T_ f,ni * \dT

(16)

«). (<)"-:? '^ X'\ dTl V'\ dT

I) < T^- dT

tf, «, 1 + 2 — +3 4 4 —

V V I' '

HT

Itf, dT2 2 '01 d-C

IV \ dT2

dC

dT

I r d2D 2djj_

d T2 ' d T

(17)


Specific Volume of Saturated and Superheated Vapor - This property at all vapor states (Appendixes A and B) was computed from the virial equation of state (Eq. (14)) by a trial and error solution.

Enthalpy and Entropy of the Condensed Phase - These properties of the saturated liquid (Appendix A) at each temperature were obtained by subtracting the enthalpy or entropy of vaporization from the corresponding properties of the saturated vapor.

Thermodynamic Properties of Sodium by the Virial Method (Liquid Path)

Expressions for the thermodynamic quantities with the properties of the condensed liquid as a base were derived directly from those in the preceding section. Those new equations together with a procedural outline of the methods of calculation are presented below.

Enthalpy, Entropy, and Specific Heat of the Saturated Vapor - The enthalpy and entropy of the saturated vapor at a given temperature were obtained by adding the enthalpy or entropy of vaporization to the corresponding properties of the saturated liquid. The specific heat at saturation was obtained by numerically evaluating at 50-degree intervals the differential

('•a \l -hf N1 NJ s NJ (18)

Enthalpy, Entropy^ and Specific Heat of Superheated Vapor - These properties in the superheat region were computed along constant temperature lines with each saturated state as a starting point. The general equations in virial form are

." irr u ' ^ ■nil

7 dD (19)

*'! * tn

\ n p . In KT

li 7 dH

V V \dT 11"

T_

2V'; dl 3 I'

T (20)

W. (d f -^-D^^-Sh^-i

V V \

in '113 , M, 1-IT— t ^V .n- <nj 2V \ ,IT

: drl w df'

}dj) .11

(21)


TaL.e 10 Comparison of Monomeric Gas and Liquid Path Calculations

(Virial Method)

Temp. i (0F)

Pressure (atm)

Monomeric Gas Path Liquid Path

h'J g s c

p I,' Ha c9

1

1625 1.0 2322.2 1.8342 0.658 2334.8 1.8400 0.640 0.2 2427.2 2.0165 0.316 2439.8 2.0223 0.298

1800 2.0 2347.9 1.7922 0.609 2357.9 1.7968 0.599 1.0 2416.3 1.8776 0.442 2426.3 1.8822 0.432 0.2 2477.3 2.0397 0.264 2487.4 2.0443 0.254

2000 5.0 2345.0 1.7216 0.591 2353.6 1.7257 0.586 ' 1.0 2491.8 1.9097 0.328 2500.4 1.9138 0.323 0.2 2527.3 2.0609 0.239 2535.9 2.0649 0.234

2200 9.0 2372.8 1.6892 0.539 2380.2 1.6929 0.530 5.0 2450.8 1.7631 0.467 2458.2 1.7668 0.458 1.0 2551.7 1.9331 0.277 2559.1 1.9368 0.267 0.2 2573.9 2.0791 0.228 2581.4 2.0828 0.219

2500 20.0 2399.9 1.6416 0.512 2400.4 1.6431 0.466 15.0 2448.3 1.6786 0.482 2448.8 1.6802 0.436 10.0 2504.2 1.7282 0.431 2504.7 1.7297 0.385 5.0 2569.8 1.8056 0.341 2570.3 1.8071 0.295 I 1.0 2628.9 1.9606 0.243 2629.3 1.9622 0.197 1 0.2 2641.3 2.1031 0.222 2641.7J 2.1046J 0.176

A Comparison of the Monomeric Gas Path and the Liquid Path for Thermodynamic Calculations

The thermodynamic properties of sodivm were computed along constant temperature lines. The starting point for a particular property could have been the absolute value of that property for either the saturated liquid or for the monomeric gas at 1 atm. As an example of using the liquid property as a base, the enthalpy of the saturated vapor at a t'iven temperature is obtained by adding the enthalpy of vaporization to the corresponding aosolute enthalpy of the saturated liquid, and the enthalpy at any state in the superheat region is obtained by adding the enthalpy change in the superheat region to the enthalpy of the saturated vapor. For the monomeric gas base, the enthalpy of the vapor at saturation or at any other pressure is obtained by adding the enthalpy change to the corresponding absolute value of the ideal gas at 1 atm. The enthalpy of the saturated liquid is then obtained by subtracting the enthalpy of vaporization from that of the saturated vapor.

Three properties (enthalpy, entropy, and specific heat) of sodium vapor were computed by both paths at selected states in the superheat region (Table 10) covering the temperature range of the measured data. The properties of the liquid for the full temperature range were obtained from Eqs. (9) and (10), which are based on the specific-heat measurements of Ginnings et al. (18) and NRL and on the absolute properties of solid

^Preliminary properties as computed by the monomeric ^as path (Z^) were based on incof' rect values for the thermal expansion of columbium-1% zirconium. They differ significantly in some cases from the final values in this report.


sodium at 32° F from the work of Evans et al. (19). The base pre parties of the monomeric gas were computed from Eqs. (6), (7), and (8), which were derived directly from the monomeric gas properties of Evans (19).

In order for the comparison of the two computational paths to be more meaningful, several points should be considered. The virial equation of state, common to both paths, was reduced from PVT data covering a pressure range o^ 1.86 to 25.1 atm and a temperature range of 1758° to 2588° F. The PVT data, therefore, effectively cover the full temperature and pressure ranges of the properties reported in AppenJix B, and only a short extrapolation of the equation is required at pressure states below 1.86 atm. Even so, small errors in the specific volume of the vapor, resulting from an extension of the virial equation or from slight inconsistencies in the virial or in the saturated vapor-pressure equations, will be reflected strongly in the properties computed along the liquid path, since these properties are dependent upon vaporization quantities. Properties computed along the liquid path at higher temperatures are also influenced by any error due to the required extrapolation of the liquid specific heat above its measured limit, 2150oF. Properties computed along the monomeric gas path are independent of both the liquid specific-heat measurements and the vaporization quantities.

The best comparison of the properties by the two computational paths can be made at temperatures below 2200°F, since this approximately represents the measured limit of the liquid specific heat. In the temperature range from 1625° to 2200° F, absolute enthalpies in the superheat region, based on the properties of the saturated liquid, were 8 to 12 Btu/lb (approximately 0.3 to O.S'X) higher than corresponding values based on the monomeric gas properties. Likewise, entropies by the liquid path were .004 to .006 Btu/lb-0F (approximately 0.2 to 0.3%) higher, and specific heats were 1 to 6% lower than those by the other path.

The relatively constant difference between the absolute property values as computed by the two paths over the temperature range from 1625° to 2200° F implies error in base properties along one or both of the two paths. There are, of course, sources of error along both the liquid and the monomeric gas paths. The properties by the gas path are dependent on the value selected for the heat of vaporization of solid sodium at 0oR (AWj)„ and on the statistical mechanical calculations for the monomer. The value of this heat of vaporization is generally derived from vapor-pressure data. From a third-law analysis of the vapor-pressure data of this Laboratory using the virial equation of state (see section entitled "Experimental Saturation Pressures"), a value of 25.61 kcal/mole was obtained, and this was used for all the thermodynamic calculations in this report. Evans et al. (19) analyzed the vapor-pressure measurements existing at that time and selected a value of 25.908 kcal/mole. If this latter value had been used for the monomeric gas calculations, the magnitudes of the absolute enthalpies by the two paths would be reversed from that shown in Table 10. It is interesting to note that an intermediate value of approximately 25.76 would bring the enthalpies by the two paths into close agreement.

In Table 10 it will be noted that the enthalpy of the superheated vapor at any given pressure, if computed from the liquid base, exhibits an abnormal decrease in slope beginning at 2200° F and becoming pronounced at 2500° F. This is reflected in the specific-heat values which at 2500°F are 9 to 21°^ lower than those computed by the monomeric gas path. Part of this apparent error in enthalpy as computed along the liquid path may have resulted from the extrapolation of the liquid specific heats above their measured range or to errors in other quantities along the two computational paths. It is believed that a part must also be attributed to errors in the enthalpies of vaporization resulting from small inconsistencies in the virial equation at higher pressures.

Engineering design calculations put prime emphasis on the change in enthalpy or entropy when moving from one state to another rather than on their absolute values; therefore, the choice of path is of minor importance for both these properties. However,


specific heat of the vapor would be expected to be more accurate if computed from the monomeric gas path, since this path is independent of vaporization quantities and does not require an extrapolation of the specific heat of the liquid above its measured range. Therefore, the monomeric gas path has been chosen for computation of all the tabular properties in this report.

Molecular Reactions in Sodium Vapor and Their Equilibrium Constants

If it is assumed that all molecular species behave as perfect gases, the association of sodium vapor can be represented by a series of independent equilibria of the type

n Va , .• K. (22)

The equilibrium constants are defined by

*„ = n— (23) CNJ".."-'

where n may be 2, 3, o 4 for the dimeric, trineric, and tetrameric reactions, respectively.

The existence of the dimeric species has been verified spectroscopically (22), but the higher-molecular-weight species have not been identified. Before equilibrium constants could be reduced from the raw PVT data, an identification of the species higher than the dimer was required. The method employed with sodium was one which has been applied frequently to the study of association in hydrogen-bonded organics (21). The apparent equilibrium constant of dimerization k'2t when all association is taken to be dimerization, can be expressed as a power series (21)

<•; k2 , 2k3p . ;^4p2 + 2ky ■ 2*2*4p3 + ••■ (24)

in terms of the pressure and the true equilibrium constants of the association reactions. The apparent dimerization constants at a given temperature may be computed from the raw PVT data, and the relationship of the apparent constants to pressure may be used to predict the higher reactions present in the vapor and to compute their equilibrium constants.

Although the posslblllti of the coexistence of significant amounts of both trimer and tetramer was recognized, the existence of only one hlgher-molecular-welght species was bellevod to be more probable. If PVT data are of sufficiently high precision, a distinction between trimer and tetramer can be made with Eq. (24). If, In a vapor mixture, species of molecular weight higher t'ian the trimer are not present, Eq. (24) (by setting ^4 o) reduces to

*• - 2klp3 -. k2 + 2kip . (25)

Likewise, If the trlmerlc species Is taken as Insignificant, the same equation reduces to

/:• + 2k2kip' -.k2 , Uy . (26)


When proper adjustments are made for the small p' term in Eqs. (25) and (26), a linear relationship between (k', ■ ik-p*) and p implies the existence of trimer, while a linear relationship between (k' * 2k2kip3} and p2 implies the existence of tetramer. Accordingly, the fit of each relationship (Figs. 10 and 11) to the experimental PVT data for sodium at 2525° F was tested. The vertical line for each data point represents the probable error assigned to each equilibrium constant. It will be noted that the tetramer relationship (Eq. (26) and Fig. 11) provides th"1 best fit to the experimental data. This was also true in a similar test made with the PVT data for potassium (la). Therefore, the assumption that sodium vapor consists of monomeric, dimeric, and tetramoric species is based on evidence from the two alkali metal systems.

Equilibrium constants for the dimeric and tetrameric association reactions of sodium were reduced from the PVT data with Eq. (26) by the same method as that described in the potassium report (la). The temperature of 2525°F was again chosen as a basis for the adjustment of the experimental data. At this temperature, k\ was plotted versus ( ipJ - 2k2i) ') on successive graphical plots until a final curve was obtained for which the intercept was not significantly different from the A , estimated from the previous plot. The factor required for each of the nine PVT experiments to correct the average molecular weight of the vapor for the apparent systematic error was computed from the deviation of k', from the best linear curve. The plot of k^ versus i 3p2 - 2k2p ') is not presented, since the equivalent plot of fAj + 2*2A:4p

3; versus p2 was presented as Fig. 11. Deviations of experimental points and the probable errors assigned to the points are not altered by the slightly different method of plotting the data.

Assuming all errors to be systematic, the apparent equilibrium constants of dimerization .<■' for each of the nine experiments were adjusted at all temperatures by the multi- plying factor obtained at 2525°F. The adjusted values of ^!, identified as f k',)*, were plotted as a function of Up2 - ik,?*) for isotherms at SO-degree intervals between 2125° and 2575° F; and the thermodynamic constants for the dimeric and tetrameric reactions were obtained from these plots. The values of each equilibrium constant were effectively fitted for the full temperature range by a simple exponential relationship in i 7 , and the resulting equations are presented in the next section.

A few experimental PVT points were obtained between 1775° and 2125° F. Since dimerization is still significant at these temperatures, the reliability of Eqs. (27) and (28) in this region had to be determined by testing the agreement of extrapolated and experimental points. Experimental values oi k , for each observed k] below 2125° F were computed with Eq. (26) (values of A-, were obtained from Eq. (28)) and these values .vere found to be in satisfactory agreement with those obtained by an extrapolation of Eq. (27).

It should again be recognized that the adjustment procedure was used only as a technique in the reduction of data. The average adjustment factor was ±0.31"? of t/,,, and in no case did a factor exceed 0.8%.

Theoretically the equilibrium constants derived for the dimerization reaction should be independent of the assumptions made regarding imperfections in the vapor, since k., for any type of imperfection is the 1 i m ^', as p ^ o. For the sodium data this was not true. The intercept or *•, for each isotherm had to be defined in part by the higher pressure data, since data at pressures below 8 atm were too few and of too low precision. Therefore, the magnitude of the dimerization constant was affected to the extent of several percent by the assumptions regarding gas imperfections.


0 022

0 020

0 014

0010 -

0 008

Fig. 10 - Plot of ( A .', - 2*3p:,J versus p for sodium at 25250F (vertical line for each point represents probable error)

0 024

0 022

0 020

0018

0 Olt)

.M 0 014

0 012

0 010

0 008

0 006 i IO 200 300 400 500 600 700

Fig. 1 1 - Plot of f ; ', < 2k Jt ,/< 'j versus p 2 for sodium at Z5250F (ve rtical line for each point represents probable error)

logÄj -4.3249+ 7204-2

log* 4 .10.67Q8 . 16-325

^KT

"' ** '


The Quasi-Chemical Equation of State of Sodium

The second equation of state of sodium vapor consists of the three equations,::

(27)

(28)

(29)

The observed specific volume data in Table 2, or the corresponding compressibility factors, may be computed from these three equations with an average deviation of ±0.26%. This equation of state, therefore, is equivalent to the virial form and may also be used to compute other thermodynamic properties.

Compositional Properties of Sodium by the Quasi-Chemical Method

Enthalpies of the Dimeric and Tetrameric Reactions in Sodium Vapor - Enthalpies of the two reactions were obtained with the van't Hoff equation

'11"J. Ml (30) ill HT2

by substituting the known differentials from Eqs. (27) and (28). The standard enthalpies so obtained are

2,Va ~(Va2, A//° = "32.948 Hlu lb-mole or-18.30 mean kcal mole

\Na ~Nav&H° - -74,661 Btu lb-mole or-41.48 mean kcal mole.

Within the precision of the measurements, each reaction enthalpy was constant for the temperature range of the observed equilibrium constant.

The magnitude of the dimerization equilibrium constant has been shown to be dependent upon the choice of the higher-molecular-weight species. On the other hand, the temperature dependency of k2, upon which the reaction enthalpy is based, is practically independent of this assumption; and a probable error of ±0.46 kcal/mole has been assigned to Ml". The enthalpy of the tetrameric reaction can be influenced by the treatment of imperfections, unless it is assumed that all simple collisions leading to inter- molecular attractions can be treated ideally as molecular association. In any event, no assignment of accuracy has been made for the enthalpy of this reaction.

The association enthalpy at absolute zero of the dimeric reaction was calculated by two methods. A value of -17.0 kcal/mole was obtained at an average temperature of 2250^ with the equation

(A//o0)2 Ml", ■ NH" ■ H^Zl (31)

Preliminary equilibrium constants (29) for the dimerization and tet rame rization reactions were based on incorrect thermal expansion coefficients for columbium-1% zirconium.


using the observed reaction enthalpy and the computed enthaloy functions of Evans et al. (19). Another value of -16.8+0.05 kcal/mole (which is an average for the temperature range from 1800° to 2400° F) was obtained with the equation

-H \n k (F0 - II') I 2

0 ! (31A) 2Vfl

using the observed equilibrium constants and the computed free-energy functions of Evans. The agreement between the enthalpy constants as computed by the two methods increases the degree of confidence which can be placed in the measured quantity and the computed thermal functions. The value of -17.0 may be compared to the spectroscopic value of -17.53 by Herzberg (22) and to the molecular-beam value of -16.91 by Lewis (23).

Equilibrium Composition of Saturated and Superheated Sodium Vapor - The relative amounts of dimer and tetramer in the equilibrium vapor and the average molecular weight of the vapor at each pressure and temperature state (Appendixes C and D) were computed by a modification of the method of Ritter and Simons (24), which was presented in detail for potassium (la). T'ie application of this method required a knowledge of the average molecular weight of the vapoi and the two equilibrium constants. With equilibrium constants obtained from Eqs. (27) and (28), the average molecular weight of the vapor at a given state was computed from the three equations

k'2 =t2 +3*4p2- 2*:,<V3 (32)

K--. 2- (33) 2

rv;)2?

tf(J = vjw, i \;( 2«,) . (34)

Enthalpy of Vaporization of Monomeric Sodium Vapor - This quantity from 1600° to 2575° F is presented in Appendix C and was computed with

AA(, = M>v-(Mi2)(x2)a - (AAi)(a-4)s . (35)

Thermodynamic Properties of Sodium by the Quasi-Chemical Method (Monomeric Gas Path)

Enthalpy of Saturated and Superheated Vapor - As with the virial method, the enthalpies of the vapor were computed along isotherms with the enthalpy of the monomeric gas

at each temperature as a starting point. Since (—j - o for a perfect gas, any change

in enthalpy must result from the association reactions; and the general equation for the absolute enthalpy is

Af = uV + \h2x2 + .-V* • (36)

The last two terms in this equation represent the enthalpy changes contributed by each species in moving from zero to some finite concentration.

Entropy of Saturated and Superheated Vapor - The general entropy equation along a constant temperature line is


/(-( V, In V, + V. In V , + \ , In S J (37)

A Comparison of the Thermodynamic Properties by the Virial and the Quasi-Chemical Methods (Monomeric Gas Path)

Enthalpies and entropies of selected vapor stales of sodium were computed by the quasi-chemical method for comparison with those by the virial method. These are presented graphically as a partial Mollier diagram (Fig. 12) and compared to the corresponding diagram generated by the virial method. Enthalpy and entropy changes along constant temperature lines as computed by both methods are in good agreement. For example, the maximum enthalpy changes by the quasi-chemical method (from p., to 0.2 atm) for temperatures in the measured range of the PVT data ^1725° to 2500°F) are an average of only LOT different from corresponding changes b" the virial method. Similarly, entropy changes by the quasi-chemical method are only 0.3^ different from corresponding changes by the virial method.

Although the two equations of state are essentially equivalent, the thermodynamic properties as computed by the virial method have been selected over those by the other method for several reasons: (a) higher confidence in the thermodynamic relationships of the virial method, (b) the appreciable error that may be generated in quantities computed from equilibrium constants and enthalpies of tho reactions by the assumption of linear relationships for the variation of log ki with 1/T, and (c) the relative simplicity of the calculation of the specific heat of the vapor by the virial method. All the final thermodynamic properties of sodium in Appendixes A and B and in the Mollier diagram (Fig. 13) were computed by the virial method.

2700

2600

D I- n

2500

I

.■

2400

2300 2 20

ENTROPV iBTU/LB0FI

Fig. 12 - Comparison of partial Mollier diagram for sodium by quasi-chemical method with that by virial method

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ENTHALPY (BTU/LB) Fiü. 13 - Mollier diagram of sodium vapor


DISCUSSION OF QUASI-CHEMICAL TREATMENT AND COMPOSITIONAL INFORMATION

The PVT results have been satisfactorily interpreted by a quasi-chemical approach assuming that sodium vapor is an ideal mixture of monomeric, dimeric, and tetrameric species. This physical picture of the vapor is based solely on the thermodynamic analysis of observed PVT results. The existence of the dimeric species has been verified spectroscopically (22), but the tetramer has not been identified by any other type of measurement. It was recognized that other molecular states of the vapor with their corresponding formu- las might be equally as effective in a treatment of the data. As a test of this hypothesis, tVj sodium results were analyzed as an imperfect mixture of monomeric and dimeric species.

The van der Waals equation was chosen to treat the gas imperfections (interactions 01 atoms or molecules not leading to stable assemblies). This equation of state

V.RT — (38)

for an imperfect vapor with a dimer equilibrium was derived by Vukalovich et al. (28). The value of bl, which represents the excluded volume correction, can be reliably estimated from the condensed volume (la). The mixture law used by Vukalovich in deriving the internal pressure term a, v2 is not valid for metal vapors, and o, would be expected to vary with both composition and temperature. However, since the dimer content of the vapor is small and the reduced temperature range is short, the coefficient o, has been assumed to be a constant. The value of this coefficient cannot be estimated theoretically and must be obtained empirically by fitting Eq. (38) to the PVT data.

The objective was to see whether or not another physical state of the vapor would cor- relate the PVT results, and no attempt was made to determine exact equational fits. How- ever, it was readily apparent that a value of a, for Eq. (38) could be found for which the corresponding dimerization constants were independent of pressure along isotherms over the full temperature range. It was concluded that an effective equation of state could be obtained in terms of »he van der Waals relationship and the ccrresponding equilibrium constants of the dimerization reaction.

A direct implication of this analysis is that several physical states of the vapor, including an Imperfect mixture of monomeric, dimeric, and trimeric species, would also satisfy the PVT data. This is not surprising. Although these gas imperfections may in reality result either from the interaction of species or from molecular association, they are all close approaches of atoms or molecules and differ mainly in longevity or average life of contact. This study of molecular models only serves to emphasize that imperfections of either type may be properly treated from the thermodynamic standpoint a.; interactions or as associated molecules.

All applications of the molecular composition information for the vapor states of sodium (Appendixes C vnd D) should be made with full realization that all values are based on the most probable model or on the most probable set of assumptions regarding imperfections. If, at a later date, the higher-molecular-weight species is positively identified to be other than the tetramer or if it becomes possible to partition the interaction imperfections from association, the PVT data can be readily reanalyzed using the correct model.


DISCUSSION OF THERMODYNAMIC AND ENGINEERING PROPERTIES OF SODIUM

The engineering and thermodynamic properties of sodiurr, ! which are presented in Appendixes A and B and in the large Mollier diagram (Fig. Ij), were computed by the virial method and are based on the monomeric gas properties at 1 atm. Two basic relationships, the virial equation of state and the vapor-pressure equation, were used with the thermodynamic equations to derive the superheat and saturation properties. The virial equation was reduced from PVT data covering a pressure range of 1.86 to 25.1 atm and a temperature range of 1758° to 2588° F. The satura. d vapor-pressure equation represents data covering a pressure range of 1.00 to 23.82 atm and a temperature range of 1618.6 to 2539° F. Thus the observed data effectively cover all states in Appendixes A and B, and only short extrapolations with Eqs. (1) and (14) are required for the pressure states below 1.86 atm. In contrast to ♦he compositional information, these properties are completely independent of any a inptions made regarding imperfections. They have been examined and evaluated by several tests for internal consi tency and by duplicate calculations using two independent equations of state. It is believed that they represent the best values and that they will be satisfactory for any type of calculation required in the design of turbines using sodium as working fluid.

The present study represents the only known PVT measurements of sodium. How- ever, there are a number of publications in which thermodynamic properties of the vapoi have been computed from saturation pressures, spectroscopic data, and published thermodynamic functions of the monomeric and dimeric vapors. The properties derived in this report from the PVT study were compared with those derived in two recent publications by Makansi et al. (25) and Weatherford et al. (26), and the overall agreement is good. If we arbitrarily take the NRL data as a reference and compare at each temperature enthalpy and entropy changes from pa to 0.3 atm, the enthalpy changes reported by Makansi are 5 to 20% lower and the entropy changes on the average differ by 1.4%. By a similar comparison ( ps to 0.2 atm), the enthalpy changes reported by Weatherford are an average of 8% higher, and the entropy changes differ by ±0.6%.

As background for the present study, thermodynamic properties of sodium vapor were computed at NRL (27) using the saturation pressures of Makansi et al. (8) and the thermodynamic functions of Evans et al. (19). If we again take the properties derived from the PVT measurements as a reference and compare at each temperature the enthalpy and entropy changes from p, to 0.2 atm, the enthalpy changes estimated previously are an average of 11% higher, and the entropy changes are an average of 3.9% lower than thosr observed in this report.

Saturation pressures of sodium were measured between 1437° and 2539' F with the null-point apparatus. This method, which is new to the measurement of saturation pressures at high temperatures, has been shown to be cap.'ble of high accuracy. The precision and internal consistency of the saturation measurements are attested to by the small variation in (Min0), as computed for all the vapor-pressure data and by the small deviation (tO.37%) of all measured data from a simple three-term equation. In the previous study on potassium (la) an equation of the Kirchhoff type was effective in fitting the saturation pressures. This study with sodium reaffirms that an equation of this type is required to describe accurately the dependence of vapor pressure on temperature.

Densities of the condensed phase were measured in the temperature range from 1577° to 2491° F with pycnometers. This method was time consuming since an independent measurement was required at each temperature point, but results of unquestionable accuracy were obtained. With these new measurements and those generated by several

^Preliminary tables of thermodynamic properties (29) were based on incorrect thermal expansion values for columbium-] % zirconium.


other investigators at lower temperatures, overlapping determinations have b ?en made from the melting point to 2491° F; and the density of liquid sodium is well defined for this full temperature range.

The specific heat of the condensed phase was measured from 212° to 2140° F. Values at intermediate temperatures from 212° to 1200° F were measured under ideal conditions and are in good agreement with the specific-heat data of Ginnings et al. (18), The .alues at higher temperatures were measured under less ideal conditions with relatively high probable errors, but they do tend to substantiate an extension of the specific-heat data of Ginnings. A more accurate knowledge of this property above 2200° F is needed.

The liquid metal program at this Laboratory is only a small part of the total national effort in this area. The internal consistency and the confidence limits of the properties of sodium, potassium, and cesium can be more fully evaluated as additional properties are measured for the three metals. Particularly important in this respect would be reliable determinations of the heat of vaporization, the specific heat of liquid and vapor, and the electrical conductivity of the vapor. A direct determination of the heat of vaporization would help to evaluate the thermodynamic computation of this quantity from the Clapeyron equation. Similarly, a direct determination of the specific heat of the vapor would test the values computed from the virial equation of state, and a determination of the electrical conductivity would provide additional information on the degree of ionization of the vapor.

ACKNOWLEDGMENTS

The authors wish to express their considerable indebtedness to Mrs. Janet P. Mason of the NRL Applied Mathematics Staff for computer programming and to Samuel H. Cress of the NRL Metallurgy Division for spectrochemical analyses of metal samples. The authors are also grateful for the consultation and advice of Thomas B. Douglas, Charles W. Beckett, and Harold W. Woolley of the National Bureau of Standards and Edward A. Mason of the University of Maryland.


NOMENCLATURE AND UNITS

H second virial coefficient, cu ft/mole

C third virial coefficient, (cu ft)-'/(mole)-

I) fourth virial coefficient, (cu ft) /(mole)'

r specific heat at constant pressure, Btu/lb-T

d density, Ib/cu ft

f free energy, Btu/lb

F free energy, Btu/lb-mole

h enthalpy per unit mass, Btu/lb

A A enthalpy change per unit mass, Btu/lb

AA2 enthalpy chango for the formation of a unit mass of dinier from monomer, Btu/lb

AA4 enthalpy change for the formation of a unit mass of tetramer from monomer, Btu/lb

AA,, enthalpy change upon vaporization of a unit mass at equilibrium, Btu/lb

AA enthalpy change upon vaporization of a unit mass of monomer, Btu/lb "i // enthalpy per mole, Btu/lb-mole

AW enthalpy change per mole, Btu/lb-mole

AH2 enthalpy change for the formation of one mole of dimer from monomer, Btu/lb-mole

AH enthalpy change for the formation of one mole of tetramer from monomer, Btu/lb-mole

AWt, enthalpy change upon vaporization of a mole at equilibrium, Btu/lb-mole

j any unit conversion

ic equilibrium constant

k'2 apparent equilibrium constant assuming only diatomic and monatomic species

w molecular weight

v mole fraction

P absolute pressure, atm

/? gas constant

a entropy per unit mass, Btu/lb-0F

A« entropy change upon vaporization of a unit mass at equilibrium, Btu/lb-0F

/■ absolute temperature, 0R

t temperature, 0F

v molal volume (normally per formula weight of monomer), cu ft/lb-mole

ii specific volume, cu ft/lb

a compressibility factor, pV'HT

Subscripts

<i quantity for equilibrium molecular mixture


« quantity for the vapor in a state

o quantity at 0oR

p constant pressure change

x quantity at saturation

' constant temperature change

i quantity for monatomic species

2 quantity for diatomic species

3 quantity for triatomic species

4 quantity for tetratomic species

Superscripts

</ quantity in gas state

t quantity in liquid state

o standard state, 1 atm for gas

apparent quantity, when assuming only diatomic and monatomic species

• adjusted value

REFERENCES

11. a. Ewing, CT., Stone, J.P., Spann, J.R., Steinkuller, E.W., Williams, D.D., and Miller, R.R., "High-Temperature Properties of Potassium," NRL Report 6233, Sept. 1965

b. Ewing, CT., Stone, J.P., Spann, J.R., Steinkuller, E.W., Williams, D.D., and Miller, R.R., "High-Temperature Properties of Cesium," NRL Report 6246, Sept. 1965

2. Ewing, CT., Atkinson, H.B., Jr., and Miller, R.R., "Quarterly Report on the Measurement of the Physical and Chemical Properties of the Sodium-Potassium Alloy, V" NRL Report C-3201, Dec. 1947

3. Ewing, CT., and Grand, J.A., "Measurements of the Thermal Conductivity of Sodium and Potassium," NRL Report 3835, Aug. 1951

4. Lewis, G.N., and Randall, M., "Thermodynamics," New York:McGraw-Hill, p. 458, L»23

5. Bowles, K., and Rosenblum, L., "Vapor Pressure of Sodium from 0.5 to 120 Atmos- pheres," NASATN D-2849, May 1965

6. Sowa, E.S., Nucleonics 21(No. 10):76 (1963)

7. Kirilov, P.L., and Grachev, N.S., Inzhererno-Fizicheskiy Zhurnal 2:3 (1959)

8. a. Makansi, M.M., Muendel, C.H., and Selke, W.A., J. Phys. Chem. 59:40 (1955)

b. Makansi, M.M., Madsen, M., Selke, W.A., and Bonilla, C.F., J. Phys. Chem. 60:128 (1956)

9. Grachev, N.S., and Kirilov, P.L., Inzhenerno-Fizicheskiy Zhurnal 3:62 (1960)

10. Hagen, E.B., Ann. Physik 255:436 (1883)

11. Ewing, CT., Atkinson, H.B., Jr., and Rice, T.K., "Quarterly Progress Report on the Measurements of the Physical and Chemical Properties of the Sodium-Potassium Alloys, VD," NRL Report C-3287, May 1948

12. Novikov, LI., Solovyev, A.N., Khabakhpasheva, E.M., Gruzdev, V.A., Pridantsev, A.I., and Vasenina, M.Y., Atomnaya Energiya 1 (No. 4):92 (1956)

13. Jackson, C.B., Wieczorek, G.A-, and Van Andel, A., "Density of the System K-Na," Appendix C in "Quarterly Progress Report on the Measurement of the Physical and Chemical Properties of the Sodium-Potassium Alloy, I" NRL Report P-3010, Sept. 1946

14. Rinck, E., Compt Rendus 189:39 (1929/

15. Nishibayashi, M., "Density and Viscosity of Molten Materials, Part 1," WADC Tech. Rept. 53-308, Part 1, Nov. 1953

36

NAVAL RESEARCH LABORAIORY 37

16. Grosse, A.V., J. Inorg. Nucl. Chem. 22:23 (1961)

17. Walker, B.E., Grand, J.A., and Miller, R.R., J. Phys. Chem. 60:231 (1956)

18. Ginnings, D.C., Douglas, T.B., and Ball, A.F., J. Res. Nat. Bur. Std. 45:23 (1950)

19. Evans, W.H., Jacobson, R., Munson, T.R., and Wagman, D.D., J. Res. Nat. Bur. Std. 55:83 (1955)

20. Hirschfelder. J.O., Curtiss, C.F., and Bird, R.B., "Molecular Tueory of Gases and Liquids," New York:Wiley, 1954

21. Johnson, E.W., and Nash, L.K., J. Am. Chem. Soc. 72:547 (1950)

22. Herzberg, G., 'Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules," 2nd ed., New York:Van Nostrand, p. 499, 1950

23. Lewis, L.C., Z. I'hysik 69:786 (1931)

24. Ritter, ILL., and Simons, J.H., J. Am. Chem. Soc. 67:757 (1945)

25. Makansi, M.. Seike, W.A., and Bonilla, C.F., J. Chem. and Eng. Data 5, 441 (1960)

26. Weatherford, W.D., Jr., Tyler, J.C., and Ku, P.M., 'Properties of Inorganic Energy-Conversion and Heat-Transfer Fluids for Space Application," WADD Tech. Rept. 61-96. Nov. 1961

27. Ewing, C .. otone, J.P., and Miller, R.R., 'High Temperature Properties of Sodium, First Qu u'erly Report for period ending 30 June 1960," NRL Memo. Rept. 1069, July 19C't

28. Vukalovich, M.P., Ni vikov, LI., Lebed, D.V., Siletsky, V.S., Dzampov, B.V., Zubarev, V.N., and Rasskasov, D.S., "An Investigation of the Thermodynamic Propertirs of Imperfect Gases," in the "Proceedings of the Joint Conference on Thermodynamic and Transport Properties of Fluids," London:Institution of Mechanical Engineers, p. 91, 1958

29. Stone, J.P., Ewing, CT., Spann, J.R., Steinkuller, E.W., Williams, D.D., and Miller, R.R., "High Temperature Properties of Sodium, Potassium, and Cesium - Fourteenth Progress Report for period 1 January to 31 March 1964," NRL Report 6128, Aug. 1964

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APPENDIX B

THERMODYNAMIC PROPERTIES OF SODIUM VAPOR (Monomer Gaa Base)

" .,II • Jail •II e ll ,

1"' (\P , , 'I ll '' ti4,1'~Jf\ ,i02\2 23ttl.95 1,83896 ,6704 1600 . • b (. Qil 14,';1~31 ,91211P :?331.76 1.!156~ ' .6264 1"' u~' . .6 ou ~ 1 01,'lt>93 ,93334 23511.77 1.!19211 ,' 5365 1~ cn , • • r, u~"~ 156,lt>41 ,95480 ?388.98 1,94008 ,4362 1"- 0'J . ,4/ f!<J •i 319,t-15 f1 • 97708 ?419.13 2' 01263 ,3285 1"2 ~ . ' • f) :\ 1! 7 •;7. ~~69 , 89916 :?318.31 1,82978 ,6690 H2 '5 , 1. 0: 511,7.:74 .110200 :»322.21 t,834U • 65113 lf\2!>. , !: OfJ to,1•6b .919 9 7 23.C6.91 1' 86356 ,5160 1A;> 5 , .6 roon 103,e-1il1 .93890 :?372. 76 1,89901 ,5034 HO'~. .• t ~ 1!>8,6 .. 41'l .95864 239~.58 1,94520 ,4128 1111! 5 . ,,. r 324,146•1 ,97905 24:?7.19 2.016!12 ,3164 1"'!> fl . l .1• !o? )1,4 .1. 07 ,89624 ?319.7 0 1. 820118 ,6669 1"5 1' , 1 . 0001 110. \•!>,6 .90964 23 311.15 1.14175 ,6174 111!> 0 , .e 0 · 71, !>11 71 ,92638 :i'361.09 1,87033 ,5498 1"'!> 1' , , , r· n 1 n,,4lll'l ,94390 23114,97 1,90490 ,4742 1•!> 0 . '• r.,ln 11>1,l i J4 .9t207 240'1.6.C 1,94999 ,3923 1" '!> 1• . • i/1: uc 3i!ll,l:l i! J3 ,98081 ;1434,96 2.02023 ,3051 1!'>75. 1. J 7 ... .,,11122 . !19J34 13?.1.14 1. 81225 ,6643 167!>, 1 . ~ r o l'l<t,l49S .91659 2353. 12 1,84880 ,5803 1"'7 5 . • "''U I

79' (1081 • 93211 2314.43 1,87661 ,5174 11\7 !>, , ~ n or• 101,1767 .94840 2396,50 1,91033 ,4483 1"' i5 , • •r c r> 1t>J,6061 • 96516 :?419.22 1.95451 ,3743 1";7!>, , i/ (•Un 3JJ, U!>i!ll ,91!231 ;>442 . 49 2.02371 ,2965 17 00 . 1 ,4 °1 ° 41,<tc25 .89047 23:i'2.63 1.80;)89 .6611 17 0!J , L ~On 6J,.) li .92292 23'17.;>0 1.85536 ,5466 17 0 , • I' H• r> 8Q,J8J~ ,93743 23~o.99 1.18246 ,4114 11ro . • 6 0 ' 1118,1!'1!>9 ,95246 24oH,41 1,91541 ,4254 11 1. n , • " r. (' ~ 16'),\ 9/8 .96793 2428.38 1,9!1177 '3!114 1 ?u r: . • 2 0 l' 3 .17,438 ~1 .98380 2449,80 2,02718 .uu 17£5. :. • e~ e" H, fJ 621 ,8816~ i'3"4.17 1.79579 ,6573 172!>, 1. oco n 64, .. 439 .921168 2HO ,48 1,86141 ,5163 1725 . , fi( I ~ 111' 7266 ,94219 2398.87 1,88793 ,4626 1n5 , • ~ (I " 110 ,!>!lil 3 • 95612 2H7, 79 1,92019 • 40!11 172!>. . •no n 16II,J!)3 1J ,97043 24~7.16 1o 96281 ,3444 172!>. .nun J41.~d60 .98507 24i6. 91 2,03046 ,2111 175 0 , l.ll ') \1~ JJ,'I07J .88483 2325.76 1.78794 .65:10 175 ft , 1. uno~ 65,!>492 ,93392 2H3.'J4 ~,86719 ,4119 17.,rJ, .b l' lifl :U, il,.0 3 ,94650 2410.14 1,89306 ,4;195 1 7'5 11 , . 6r on 112.<t.t.S5 • 9'5944 ~427.69 1. 92469 ,3170 175 !1 , ,<~ no n 11U,6/5~ ,97269 2445.61 1,96666 .nu 175 . • 2 r, t:n 340,1 001 ,98622 <!463,86 2oOU62 ,2748 17 75, :.-. u74 P JU,11178 .18206 2;127,41 1o 711032 ,6482 177 '5 , i', O ,,I" 31, 44.'93 ,1)8557 ;>332.24 1. 78526 ,6396 17 7!>, 1. 0Cu " ~6, 6:.!97 ,938,.9 2404.95 1,872!1~ ,4644 177 5 , • eno. 84,J:Uoi ,95042 2420.87 1o 89789 ,4189 177 5, • 6 t'(J ' 1tJ,85iP ,96244 24.57.16 1,92896 ,3710 17 7, , • •r'''"' 112,96117 , 97473 24 53.76 1.97033 .3209 17 75 , • 2 ! ,, 3,U,3t140 ,98726 2470.66 2,03661 ,2691 1@0 . C:,3r A 27,3441 ,117932 2329.11 1. 77295 ,6430 1~ Pr. , c. on~n J2, 0457 • o9294 2347,85 1,79221 .6094 11' 00 , 1. C· r.c n 67,6876 ,94J05 2416.27 1,87759 ,4422 1• on . , 1\ ~p n 85,51105 ,95391 2431.11 1,9024!1 ,4005

3t

40 NAVAL IESEAICH LAIOIATOIY

APPENDIX B

THERMODYNAMIC PROPERTIES OF SODIUM VAPOR (cont'd) (Monomer Gas Base)

, •' • fill •' ell ~

itOO O, !:t, •IIJ U• 13,4166 .8'!i863 2345.00 1,72163 ,5911 21)0 0 , 4, or· on 11,21.55 .88130 2.57'5. 74 1,75090 ,5626 otiJo n , 3. •Jnu o 2.s, &<~ :s~ • 911710 2410.81 1,78739 ,'5070 200 \l , 2. ~ ~0~ 36.~54'J .93576 ?449.70 1.135'51 ,4273 2no a . 1. no 75, 5 4~4 ,96688 2491 . 79 1. 90961 ,3284 200 0 , ·" r.u 95,C~82 ,91336 <'500.'53 1,93194 ,3061 2 11 00 , • ft r~ 0 ' l 121,511n , 97991 2509.37 1,95981 ,2847 211o n . .• ~ a~ 192,6111.5 ,98654 2518.29 1. 99789 .2622 2!10 0 . • , ,. 0 •1 ~57.911~6 ,99324 25?.7.31 2,06011'5 ,2393 2025, 5,4ilo94 12.~!:>02 .85589 2346.89 1,7157'5 ,'5142 202'5, 5, 01 IJ~ 1-',1!-=>d5 ,86532 23'59 , 61 1,727'53 ,5768 2025, 4, ~ 11 0~ 17,~U<.IS ,118744 2J.,9.57 1,75649 ,'5437 2'l2'S. 3 o (oli O l!J,II II a7 ,111224 242.5.~4 1,79242 ,4177 202'5, 2, tno J/,li1 J6 ,?3950 2460.18 1,U97'5 ,4117 202'5, 1 ; ~. on 1&,46'511 .9o888 24911,89 1. 91296 ,3196 2025. .& c on t6,n!J1 • 97497 2!i 08 .11 1,93501 ,2996 202'5, , 6LO tol!\1, 0'>57 • 98114 2!H6.42 1. 96266 .2793 2 r. 2!1. • 4( 0•' 194,812~ .98737 2524.110 2,00052 ,2185 202-;, ,2 ro o 3~i!.l il i\ O ,99365 25JJ,26 2. 06326 .2374 205 fl , 5.9 !-~ " !1,• :.. 27 .85336 23<19.09 1,71028 ,'5713 2n5n, 5. ooo n 13,b<l85 . 87175 2.513.83 1, 73323 ,5614 2ns ~ . 4, COOt• 17,1! Ul6 ,89325 2402.93 1, 76184 ,'52'51 20'5 ~ . 3. U~O~ 24,;st-tl n ,91706 il4.!5.20 1. 19721 ,4696 211'5 . it. or• on J"/,!:1 349 ,Y4297 247U.29 1,84379 ,3973 205 11 , 1. on 77,3114! , 9 7072 25117.78 1,91612 ,3116 2 0'5 0 , ,e ro~ 9/,29911 • 91646 25t5.52 1,93797 ,2931 205 . , to !I O ,, 1.SU,50;s9 ,9t1226 2523.34 1,96543 ,2143 2n51 , • 41•00 1116,94!3!1 .98812 25 .11.22 2,00309 ,2552 21)5 n , .2 ~011 3116,20.56 • 99404 25.59.18 2. 06563 .23"7 20 7'5, 6,4 ~ 4'5 1U,!:t6J7 .~5083 i'H1 • .51 1,70496 ,5705 ~ 0 7">, 6, 0110~ 11,5ol!llt'l ,85916 2362.44 1,71501 ,5664 2 17'>. 5. oc on 14,1.561 ,87791 2387,o7 1. 73872 • 54'53 2n7!>. 4. 0(! 00 111, Qtl94 .89874 24 l.5.113 1,76696 • 5011 207';, 3.~ ~0, 24, 7J15 ,92155 2446,73 1,110171 ,4527 207'1, 2. O'JOIJ ,,8,0 890 .94619 2480.06 1,84767 ,3842 207 ? , t. uoon 18,i!d98 ,97242 ?515.47 1,91917 ,3043 2n7 !> , ,t~ n on 'itl,4074 ,97784 :1.'522. 77 1,94085 ,2872 2075, ,"J c On 1.51..,9435 • 98331 25.50.14 1,96813 ,2698 207!', • 4 'l 01 1Y9,0l':i9 ,98882 25.!7 ,56 2,00561 .2522 2075, • ~ 'i 0 '' 400,292? • 99439 2545,05 2,06796 ,2342 210 0 , 7, J4 24 9. 711.55 .84829 2353.56 1,69978 ,5639 210 0 , 7. nu ~ 9,8&1)4 ,84895 2354,43 1,70056 ,'5637 210 C, 6. 0"0 11,7'U6 .86546 ?376,45 1,72058 ,5536 210 0 , 5. on o 14,,5 '111 . 811378 0'41)1.10 1,74399 ,'5290 21.0 0 , 4 . ot·o~ 18,3129 .90391 ?428.29 1. 7718'5 ,4898 210C, 3. 0 OIJ 2:;, oa9.5 ,92576 ~457.85 1,80614 ,4J69 210 0 , 2. or.on 38,5!!1S2 • ~4918 241'9.51 1,85138 .3722 2100, 1. uo o '19,1 'J~O • 97400 2523.00 1,92212 ,2977 21.0n, ,f' ,>OIJ 9Y,; u71 • 97 911 2529.ti9 1,94364 ,2119 210 0 , • t-- t' Un tJJ,J/51. ,911427 25~6.83 1,97076 ,26'58 2100, '" '' U 2 •ll,1i! 02 .98947 2543.83 2,00807 ,2494 210 0 , • ~ '' 0 ~ 4U4,l126 ,99471 2550.89 2,07025 ,2328 2125. 7. t. - ~ ~~ II,O YH .84573 2355.81 1,69474 .'5974 212'5, 1, or· o~ 10.0JJ8 .85526 2368,41 1,70600 ,'5544 2125, 6.~ ~ o n 11. 92':it .87152 1.590.12 1,72590 ,'5399 212'5, !>, ur on 14,61J J 1 .ct8937 2414.12 1,7490'5 ,'5UI 0!125, 4,(1 (,00 18,6!:>.!3 ,9·0878 2440,33 1,77653 ,4733 2125, J. or oo 2t;,4418 ,92968 2468,511 1e81032 ,4222 212'5, 2,C COO JY,U/11 • 95196 2498.68 1,85494 .:stu 212'5, 1, 0 (· 0~ 8U,U!IJ2 ,97545 2530.36 1,92499 ,2911


APPENDIX B


212b. .«( Q' 2\2*. , 6 r u o 2125. ,4roo

212'5. .2i.00 81-50. H.r^i« 2l5tj. 8. u o 0 0

2190. 7.0 'U-1

2150. 6 , 0'. 0 o 2150. 5 . 0 - 0 n

2150. *.uyr 2150. J . 0 ■ 'J ' 2150. 2,0 0 00 215". l, o r in 2150. .8-j- 2150, , 6 '.' L " 2150. .4CG1

2150. • J-J"

2175. 8,9?J5 2175. b. ü n on

2175. 7,0f,0n

2175. ft.UtO" 2175. 5 . 0 o [i .1

2175. 4, o o o n 2175. 3 . 0 r u 0 2175. 2 . 0 'i a 0 2175. 1.0000 2175. ,«!' 10 2175. .6JÜ0 2175. . 4 i j n

2175. .2 lüi 2200. 9.6«C0 2200. »,0 0" 2200. 8,0001 2200. 7. J0Ü0 2200. ft.O'iOO 2200. 5.0"üO

2200. 4.Ü"IJ") 2200. 3. 0'. ü i 2200. 2 . o ;■ o T 2200. I.O'JSO

2200. .H'-m

2200. , 6 ^ n o 2200. . 4 ■• C 0 2200. ,2''C" 2225. io,a»-»« 2225. IO.OOUO 2225. * , 0'' o n

8?25. 8 , 011 b n 2225. 7 . 01 U 1 2225. ft . Ü r' b 0 2225. 5.pnci 2225. «,üroo 2225. 3 . 0 f 0 " 2225. 2 , 0 u 0 0 2225. I. U n 'J i" 2225. ,8000 2225. ,6000 2225. ,4000 2225. , 2 r. c o

2250. 11,1789

h»

10(;.5VV7 I34,7v«b 20J.2U/1 408,4453

fa. 45'}/ 8.7/4^

1U, 20(15

1^,1208 14.bJ22 ld.9t/7

25,78V3 3^.5023 811,969»

101, 6 c 5 V 136.21/1 205,28/2 412.5115

/,8/39 8,9225

10,3*90 12,3144 15.U5Ö3 l'i(.19V? 26,1321

40,0420 81,85'J5

102,7656 137,6285 20/.3610 416.5/12

/,3423 /,V3V3 1», 0 / 01

10,5352 12.5055 15.2H15 19.4664 26.4/09 40.51f)(S 82, 7257 103.839» 139.0344 809,4292 420.62bl

6. 8'J'36

7.16.4

8,0/05 9.2169

10.7019 12.6951 15.5017 19,731.) 26,8047 40.9867 83.5958

104.9091 140,4350 211.4921 4 24.6/57

6,4092

.98028 2556 .87

.9^516 2543 .43

.99007 2550 .04

.9950? 2554 .69

.Ü4315 2358 .08

.34681 2362 .86

. 16140 2382 .14

.H7734 2403 .44

.89467 24J4 .74

. iil336 2451 .96

.9T335 ?47B .97

.«5454 2507 .58

.97681 25V .59

.98137 2543 .74

.'JB598 2549 .94

.99062 2556 .18

.99529 ?5'>2 .47

.84054 23^0 .34

.85294 2376 .53

.66732 2395 .58

.88290 2416 .40

.89969 2438 .97

.91767 2463 .22

.93679 2489 .02

.95695 2516, .23

.97806 2544 .68

.98239 2590, .50

.98674 2556 .37

.99113 25ft2, ,27

.99555 2566, .21

.81789 2362, .59

.34580 2372, ,81

.85891 2389, ,98

.87303 2408. ,71

.88820 2429, ,00

.93444 2450, ,83

.92172 2474, ,12

. .MOOO ?«98, ,77

.95919 2524, .66

.97923 2551. 65 ,98333 2557. 17 ,98745 2562. 72 ,99161 2548, 31 ,99579 2573. 94 ,83520 2364. 82 3)969 2370. 56 85177 2386. 19 86466 2403. 17 87849 2421. 52 83324 2441. 25 9J893 2462. 32 92583 2*84. 68 94300 2906. 24 96129 2532. 89 98031 2558. 51 ^8420 2563. 74 98811 2549. 01 99205 2574. 31 99601 2579. 63 83245 2367. 02

■ » <

1.94636 .8770 1,97332 .2681 2.01048 .2469 2,ii725l .2319 1,68983 .5913 1,69404 ,5909 1,71128 .9439 1.73102 .5297 1,75391 .4970 1,78101 .4977 1.81438 ,4066 1,85637 .3509 1.92777 .2662 1,94900 .2786 1,97583 .2587 2,01285 .2446 2.07473 .2304 1,68504 .9494 1,69926 .5486 1,71641 .5319 1,73997 .9118 1,79696 .4616 1,76930 .4430 1,81819 .3999 1,6610' .3416 1,93047 .8818 1,95196 .2689 1,97826 .2996 2.01917 .2426 2.07698 .2294 1.68036 .9400 1.68981 .5393 1.70434 .5326 1.78137 .5169 1,74073 ,4969 1,76306 .4669 1,78948 .4891 1,88183 .3648 1,86489 .3330 1.93311 .2766 1.99410 .2646 1.98066 .2586 8,01749 .8407 2,07909 .8284 1,67980 .5349 1.66069 .5390 1.69488 .5319 1.70987 .9280 1,78616 .9099 1.74931 .4628 1.76736 .4986 1,79337 .4161 1,62936 .3733 1,66793 .3891 1,93567 .2784 1.99696 .8614 1,96303 .8908 2.01969 .2389 2.-6188 .2879 1.67133 .5304


APPENDIX B


k*

2?5n. U.'irM 6,5207 .83440 2369.48 1.67340

22,JP. 10.U'0" 7,2/04 .«•1564 2383.86 1.68562 2?9C. V . 0 ^ i' 8,2011 .8^757 ?399.37 1.69910 2250. b. 0 r o i 9,3626 .97025 2416.08 1.71406 2?5C. 7 . 0 n 0 o 10,8659 .«8373 2434.00 1,73079 2?50. 6.01 :i •; 12.8821 .09803 2403.14 1.74972

2250. i.l'-Uii 15,7190 .91317 24-'3.47 1.77149

2?5n. 4 . Ij' L' 1 19.9917 .92910 2494,93 1.79717

2?50. 3.01 Ü'1 2/.1349 .94581 2517.44 1,828/9

2?5n, 2,t.r ;p 41,4523 .16324 2540.92 1.870)1 2250, i,i'i-< «4,4612 .'>ei32 2565.27 1,93818 2250. .B' u- US,9/36 .98501 2570.24 1,95897 2250. .fr' Li 14l.8i07 .98873 2575.23 1,98534 225"'. .«r1 j" 213.55U0 . -19246 2580.26 2.02190 2250. .i1 0^ 42Ö,71/4 .9962.' 2585.31 2.Q8332 2275. 12.0:22 5,999? .bL963 2369.17 1.66696 2275. 12 . 0 ■ 'j ^ 6,0063 .82976 2349.33 1,66709 2275. 11. COi 6.6.558 .84034 2382.68 1,67629 2275. 1 C . 0 ' '11 7,3960 .H0145 2396.98 1.69044 2275. V . o - 0 1 8,3310 .86319 2412.30 1.70385 2275. b.n.nj" 9,50/1 .87560 2428.69 1.71869 2275. 7 . ^" ü 1 11,0261 .SH672 2446.16 1.73526 2275. 6.CGI 13,0668 .90258 2464.71 1,79397 227'.. 5 . Q '. 0 ' 15,9336 .91717 2494.30 1,77547 2275. 4,1-0? 20,2492 .93247 25"4.e8 1,S00A3 2275. 3,1)000 2/,4616 .94845 2526.41 1,83208 2275. 2,0.101 41,9140 .96506 2548.79 1, j/380 2275. 1, ü • J n 85,3223 .98226 2571.94 1,94063 2275. ,8100 10/,0335 ,98577 2576.66 1,96133 2275. ,«10fl 143,222] .98930 2581.40 1.98761 2275. ,4101 215,6035 .99285 2586.17 2,02407 2275. • iroo 432,7565 ,99611 2590.97 2.08940 2100. I2,ev03 5,622(1 ,62674 2371.28 1,66268 2100. 12,for 6,1045 .83569 2382.44 1,67186 2300. 11. t r o f 9.74kl8 ,84614 2395.74 1,68300 2300. lO.CCOO 7,5130 ,85709 2409.90 1,69919 2300. 9, TOT 8,4599 .86861 2424.98 1,70847 2300. 8. li f. 0 0 9.6502 ,88073 2441.01 1,72316 2300. 7,0C0C 11.1884 .89349 2458.00 1.73997 23QC. 6.C'B« 13,2492 .90689 2475.94 1,79806 2300. S.CrO" 16,1455 .92095 2494.81 1.77930 2300. 4, c r. c o 20,5035 .93563 2514.56 1,80439 2300. J.ccon 27,7849 .95091 2-J35.14 1,83526 2300. i.OCLO 42,3/19 .96677 2556.49 1,87660 2300. l.C'•0', 86,1794 .99314 2978.53 1,94303 2300. ,8000 108,089« .98648 2583.01 1,96364 2300. ,♦.'01 144,6094 .9P983 2587.52 1,98983 2300. ,400« 217,6529 .99320 2592.06 2,02621 2300. .2301 436,791« .99659 2596.61 2,08746 23<5. 13.8143 6,2/44 .62376 2373.32 1.69848 2325. U.oron 5,6581 .83159 2382.97 1.66629 2325. 12.001 6,2026 .64150 2395.43 1.67699 2325. 11.0'101 6,6493 .65180 2408.61 1.68769 2325. 10,0001 7,6294 .86255 2422.58 1.69972 2325. », Ü P 01 8,38/8 .87382 2437.38 1,71294

2325. 8. 0 0 ü 1 9,7919 .98544 2453.02 1,72791

2325. 7.ü■'^', 11,34/2 .89802 2469.53 1,74373 2325. 6.0101 13.4295 .91098 2496.87 1,76200 2325. 5,01U0 16.354H .92451 2505.04 1,78298 2325. 4,0100 20.7551 .93860 2523.99 1,80779

.530!

.5287

.522:

.510!

.492?

.469]

.4394

.403t

.3632

.317?

.268!

.2982

.247?

.237« ,226; .5262 .5262 ,525! .5211 ,912a ,498; .479? .499? .426) .392! .393? .3ii: .269C .2994 .249; .2355 .226( .522« .522! .518( .912] .501« ,486; .4673 .443: .414; ,381? .349: .309C .261« .2526 ,243; .234« .2292 .920] .919: .9164 .9111 .502! .490! ,474; .494? .4311 .4034 .372C


APPENDIX B


*»

2325. 3 . ür 'J" 2B.1U47 .95323 2543.67 1,831134 .3372 2325. 2.Ü- ij" 42,6263 .96836 2564.C4 1.87933 .2993 2325. i.c un 87,0328 .98397 ?565.03 1.94537 .2588 2325. .fa-:" 109,141« .96714 2589.33 1.96591 .2504 2325. . 6' • - 145 .9SI2S .««033 2593.59 1.99202 .2419

2325. .*.'." 219,6Vb4 .99354 25 9/.9U 2.02832 .2333 2325. .2 : o 440,«225 .9<»676 2602.24 2,0B94g .2247 235C. 1 * , 7 ( 0 * «,95i>. .8^069 2375.27 1.65435 .5181 235". 14.C'0" 5.27/9 .82795 2364.15 1,66139 .5167 235C. 13 J^I."

1 5.74H8 .83740 2395.89 1.67091 .5139 235C I2.t'u- 6,3004 .S4716 7408.25 1,68113 .5093 2355. 11. u' o" 6.95^J .85728 2421.28 1,69218 .5023 235C. 11 . 0 '' u 0 7,74<iC .8f,782 2435.02 1.70417 .4924 235''.. 9 . C' V 8.71*6 .B7883 24*9.50 1.71727 .4794 235C. b. I r o i 9.9Jil .89033 2464.75 1.73170 .4630 235P. 7 . u' u " 11,50*1 .90:33 2460.75 1,74774 .4430 2350. 6, b n n n.tun .91465 249/.50 1.76580 .4196 2350, 5 . G' C i 16.5617 .95788 2514.99 1.78654 .3928 2350, 4 . C ' ', " 21.0033 .44140 2533.17 1,81103 .3627 2350. 3,(1' (!" 26.4217 .95540 2552.01 1,84132 .3297 2350. 2. CM," 43,2//* .««986 2571.46 1,88198 .2940 2350. 1 . C ' L " ft/.6027 .96473 2591.47 1,94767 .2560 235". . b'. i n llü.iviif .96776 2695.93 1.96813 .2482 2350. .ft' w 147,372« .99080 2699.62 1,99418 .2402 2350. .4' t, 1 221.74!.« .99385 2603.72 2.03040 .2322 2350. , 21 u " 444,0449 .99692 2607.65 2,09149 .2241 2375. 15.ft 5^ 4.65/0 .81750 2377.14 1.65029 .5168 2375. lb.Of Di 4.95j4 .62470 2385.82 1.65707 .5148 2375. 14.01 in 5.362J .85377 2396.99 1.66595 .5118 23 75. 13.ü^^ ^.«3^2 .64307 2418.66 1,67543 .5074 2375. 12.0' on 6.39/7 .85265 ?4?3.e9 1.68561 .5013 2375. U.o C 7.06J^ .86258 2433.72 1.69658 .4930 2375. 10 . U " rJ "! /.8595 .87289 2447.20 1.70848 .4820 2375. 9.1" ,■ 0,84,11 .86363 2461.35 1,72147 .4683 2375. e.p^-i 10.0/09 .89480 2476.18 1,73575 .4519 2375. 7.0'!.- 11.65V? .90643 2491.68 1.75161 .431« 2375. 6 . T"'. " 13. 7H.i7 .91851 2507.86 1,76947 .4087 2375. t>. J ' 0 " 16,7663 .95105 2624.66 1,78998 .3828 2375. 4.ü-'Jn 21,2501 .94404 2542.13 1,81421 .3541 2375. 3 . C " .'■ ->8,7359 .95745 2560.16 1,84421 .3228 2375. 2 . C 0 b 0 43,7257 .97126 2578.74 1,88456 .2892 2375, i.O^OT Ha,/^4 .96545 2597.84 1.94993 .2535 2375, .80 jn 111,2362 .96834 2601.71 1,97032 .2461 2375. . 6 ' ; ^ 148,74<>4 .99123 2605.60 1,99630 .2387 2375, .4-j' 223,7/Vl .99414 2609.52 2,03246 .2317 237'., ^"O'1 448,8/41 .99706 2613.44 2,09347 .223 2«00, 16.875r 4,3B2i .81419 2376,89 1,64629 .516 2400. 16. o r o o 4.6653 .82178 2387.96 1,65323 .5134 2400. 15.0^ 5,02V4 .83054 2398.64 1,66157 .5099 2400. 14.0rü 9.4*64 .83945 2409.71 1.67042 .5056 240". 13. J'.O- 5,929? .84858 2421.25 1,6/986 .5000 2400. 12.3rü" 6,494* .85798 7433.31 1,68997 .4927 2400, 11 . t' 1. - 7.1651 .66770 2445.92 1,70087 .4833 2400. lO.IKO" /,9/31 .67777 7459.12 1,71267 .47:15 240". 9.0'ür 6,96*4 .66822 2472.92 1,72553 .4573 2400. e.of T1" 10,2081 ,69907 248/.32 1,73967 .4403 2400, V . ü'. u r 11.8125 .91032 2502.33 1,75535 .4206 2400, b.O'P" 13.95'f .92198 2517.94 1,77301 .3983 2400. b.O'C- 16,9666 .93405 2534.15 1,79330 .3734


APPENDIX B


t

> B» i *» .»

1'

2«0i. 4.0 C- 21,4Vjft .94652 2550.o« 1.91728 .3460 240r. 3.ü'0'i ?<),i* /* .93936 2568.15 1.84701 .3164 2« Of.. 2 • 0 { u ' 44.1/ll .''7257 2585.92 1,88708 .2647 2«0P. 1. £J ■ Ü '■ 8 9,!>/,^ .9«613 2 61) 4 . 1 4 1.95214 .2911 2400. • h ' u " 312.2/87 .9Ha«8 26T7.84 1,97248 .2442 ?40C. .t' y 15U.12J1 .99164 2611.55 1,99839 .2372 240^. . « ' L ' ■tii.toi«! .99441 2615.28 2.03448 .2302 2401-'. . i1 ' 1. " 452.«V3? .90720 2619.iJ 2.09543 .2231 242S. I7.VS;M 4.1^/9 .«1073 238J.52 1,64234 .5169 2425. 17.tfrii' 4.4:5? .01916 2390.49 1,64981 .5126 242b. 16.L Cl- *,7JV / .82765 2400.74 1,65767 .5084 2425. iS.f.'f 0' 5,1081 .83623 2411.31 1,66598 .5039 242'3. 14.f'.' !>. !> o 01 .84497 2422.27 1,6747» .4985 2425. 13. t ^ I - 6. uia6 .85392 2433.65 1,68417 .4919 2425. 12.C 3" 6.5VJ5 .8AJ12 2445.52 1,69422 .4836 2425. 11. r, ( o " /.2fiel7 .87262 7457.88 1.70503 .4734 2425. U. C1 ü " b.uH?ft .88244 2470.78 1,71673 .4611 24?5. 9 , '. ' ( " 9 . C 3 / 5 .89261 24M.21 1,72947 .4465 2425. H.I '0° 1'J, J430 .90313 2496.19 1.74345 .4295 2425. 7, t i" 0 n 11.9641 .91402 2512,72 1,75897 .4102 242^. 6 .'.' U '" 14,IJU0 .92527 2527.78 1.77644 .3865 2425. 5 . C ■ J " 17.1689 .93689 25*3.36 1.79651 .3646 2425. 4. 0' • C "1 21,7353 .94686 2559.43 1.82026 .3385 2425. 3. C ' ü ■! 29.3345 .96117 25/5.9« 1,84974 .3104 2425. 2.r'' t ^ 44,6138 .97381 2552.9« 1,88954 .2805 242'=. 1. . c Ü i 90.414? ,98676 261Ü.39 1,95432 .2490 242". .-".u" 113.3ld4 .98939 ;-61 3. 92 1,97459 .2425 242' . .6 u' 15J.,4V39 .99202 ?6W.47 2.00045 .2359 242'. . .4 r 227,64/? .99467 2621.03 2.0364S .2293 242* . .<:■ in 456,9134 .99733 2624.60 2.09737 .2227 245'. 1 v.: > 9 3 3.6V1« .80712 2382.01 1.63844 .5185 245f . 19.C: u" 3.9J29 .80853 2383.64 1,63962 .5175 245''. iB.Cr Of 4.1939 .81681 2393.35 1,64676 .5121 245 . 1 /. V -J ' 4.4355 .82506 2403.24 1,65421 .5073 245' . 16.jnCr 4.8137 .83335 2413.3" 1,66204 .5024 2451 . 15 . 'J ' G , 5.1564 .84176 2423.«2 1,67030 .4971 245' . 14,: • i' - 5.613» .85032 ?4^4.63 1,67906 .4908 245 . 13. J' 0" 6,10/5 .65908 2445.84 1,68838 .4833 245' . 12.(Kl^ 6,6055 .85808 2457.49 1,69835 .4742 245' . 11.i' J' 7,3/1* .67736 2469.59 1,70908 .4634 245' . U ..' tr 6.19/1 .8*692 2452.1/ 1,72066 .4507 245 . 9 . C , t ' »,21193 .99680 2495.24 1,73327 .4360 245- . 0. r,, j 10.4/83 .90700 25n8.H0 1,74711 .4192 245- . 7.C'Or 12,1142 .91753 2522.85 1,76246 .4003 i 5". t.tii C 14.3CÜ4 .9i'B38 2537.37 1,77975 .3793 245'.. 5.CO" 1 / , .■< 6 / 1 .93956 2552.37 1,79962 .3563 245 . 4. r '■ i, - 2l,C'4(, .95106 2567.81 1,82315 .3315 245 . 3.r-i' 29,6032 .96287 2583.6/ 1.85239 .3049 245-. 2.r-o- 43.054] .97497 2599.94 1,89194 .2766 2451. 1 . ( ü Ü " 91.2526 .98735 2616.39 1,95646 .2470 245':. . {"■ o r 114,3^56 .98986 2619.96 1,97668 .2409 245r . .6t 0' 152.C*^? .99233 2623.35 2,00248 .2347 245r. .''L0 2Z9.K/ n .99491 2626.75 2,03846 .2285 245-. ,2^.0 46Ui9^'>>n .9<J745 2630.16 2,09929 .2223 2475. 20.396? 3,6/1-. .80334 2383.33 1,63456 .5213 2475. 2C.10( ' 3.75V3 .80659 2387.06 1,63721 .5184 2475. 19.' TM 3,VV/3 .81470 2396.51 1,64403 .5120 2475. 16. o o o n 4.26J7 .82274 2406.0« 1,65111 .5065 2475. 1 7 . '; r & - 4.5354 .83079 2415.85 1,65652 ,5012 2475. 16. (ir Ü ? 4,11674 .83889 ?4?5.85 1,66631 ,4957

NAVAL IESfARCH LAIOIA TOIY 45

APPE. DIX B


- ---- --- - -, vii z All •II e ll ,

2• 7': . 1 !>. n ' a ,, :>,264 3 ,1!4712 243e.16 1,67452 ,4196 2« 7' • 1•, r, r o 5,b~61 .85549 2 ~46.80 1, 68322 ,4826 2£7'>, 13. " (j 6,1'1157 .86407 £1457.82 1,119248 ,4744 2·0 !> . 1 ~- ·i r v"' e.. /t11 ~ .87286 ~469,23 1 , 70237 .4647 2•7 o; , 11. \;~"!{, /,41J4 ,811190 24 81.06 1, 11300 ,4535 247 ~ . 10 . .. ~ 01 8,J U/S ,89121 2493.32 1, 72441 • 44116 247 5 , Y. (rC 01 9, :12'11 9 ,90080 ~506.02 1, 73696 ,4259 24 7 ... , 8 . 'r .. a ~ 1U,rU12 ,91068 ?5l9.16 1,75066 ,4093 247 .., , 7 _ rJu01 1.!.2 r> 2r'> ,92086 ?5 , '2. 74 1. 76511!1 ,3909 114 7'> , 6, uGl1 , 14,46'1 U ,93133 2546,75 1, 78296 ,3706 24 7" , !>. Jl " 17,!:>635 ,94209 ?561.1!1 1,80263 ,3486 24 7 '> . 4, v 'J , 22, i!119 • 95314 257ti.01 1. 82596 ,3249 24 7';.. ,) • ,, ,, 0, 2'1,\lt>/8 ,96447 2591 . 23 1,85491 ,2997 247 " · 2, ~H 0 45 ,4'~21 .97606 26 06.81 1,89429 ,2730 24 7"', l. 'J , 92, 0 '!186 ,98791 U22.74 1. 95856 ,2451 2• ., ., • . ~ n ~') t15,j'i03 ,99031 26 25.97 1,97873 ,2394 2• 7'· . ,'> PU 154, <!2 79 ,99272 2629.20 2.00448 .2336 0,4 7? , • 4 :: ~, 2.11, YU54 ,99514 2632.45 2.04041 .2271 24 75 , • (d(r 464 . .. 420 ,99756 '-63!1,72 2,10119 ,2219 2'5 0rr, 21., 77 J,4 1.> 66 ,791136 2384,46 1.63074 ,5254 2"> r; :• • J,'l UJ O .80485 2390.72 1, 63506 ,5195 c5 o•·. J, 8 ~ 0 6 .81281 2399.94 1,64159 ,5122 2 '5 0 4. ·· 606 .82067 ?409.24 1,64135 ,5060 25 QII , 4,J ;!/O .82849 2418.67 1. 65531 ,5002 25 011 , 4,6 <1 49 ,83634 £1428.29 1,66275 ,4944 t's; l) J , 4,91.106 ,84427 ?4 38.16 1,67048 ,4884 25 011, 5,3417 ,85231 (1448.30 1,67164 ,4816 2'i •) ~ . 14. ~ r·o ~ '>,7182 .86050 2451,76 1.61721 ,4740 2'> •11 . 13. 0CU 6,2 11.! 2 .&6887 24119.56 1.69646 • 4653 2'5 0 l . 12. CC'O~ 6. ~ 141 ,87745 2480,73 1,70627 ,4553 2'5 1) '1 , 11. ur " 7,5 i 43 .88626 2492.27 1,71680 ,4438 2'i OIJ , 10 . c 8,4168 • 89531 2504.21 1,72817 ,4307 2'5 0Q, ~. O ' L ~ 9,44\12 ,90462 2516.54 1,74053 ,4161 2'5 0~ . b . ,_. 1 11 .7428 .111419 252\1,27 1. 75409 ,3998 25 nn , '1, C C l>~l 12 ,4 U9 5 ,92402 ~542,40 1,76913 ,3819 25 0 . ~. orc.n 14.&J6 0 • 93412 2555.91 1,78607 ,3624 25 011 , !>, o ru~ 11,7'>81 • 94448 25 69,80 1,10556 ,3413 2'5 0 ", nrc.~ 22 •• 472 .95510 25ll4.06 1,12869 ,3181 25 0 11 , :! , l' ' c 30,2/03 ,96598 2598.66 1, 85750 ,2949 250 0 , . ;.. . o~ 1" 4!1,9<1/9 • 97709 261.).60 1,19659 ,2697 2 '50 0 , 1. trr.u 112,'1<12• • 98844 2628.8'5 1,9~64 ,2434 (1<; 0(1' • b r ~ , 116,•22 1! ,99073 t!&31. 93 1,98076 ,2380 2s; oo . • 6 f (i fl 15:»,5'11 5 ,99304 2635.03 2,00646 ,2325 2s; o . • • C• l' 2JJ,9 .508 ,99535 :»638.14 2,04234 .2271 il'i OII , • i' t'fl ~ 4611,9? 211 ,99167 ?641.26 2,10307 ,2216 2 ~25 . :1 3. 0 5*' J,V!I• • 79517 23115,38 1. 62693 ,5310 2 52~. ;>J, {I (I ~ ~. 21111 ,795;,o 2J85.53 1,62702 ,5308 2~2 5 , 2~ . 0 or• :.4'!117 ,80331 '-394.60 1,633\3 ,5201 2525, 21, (I ~ 0 ~ J , 6618 .IU113 2403.62 1,63940 ,5126 252 '5 , t' (r, 0 r. (lr• 3,11 !1 13 • 81881 '.412 . 67 1,64587 ,5056 2'52 5 . 11•. ~c n 4,1<!37 .82644 2421.80 1.652!17 ,4993 20,? !> , lt. Or O" 4, 3'10!9 .83406 24~1.09 1,65956 ,4933 2'52 :'> . 17 , nrr,r· 4,6Y• o ,84172 2440.56 1.66687 ,4171 2 '52'5 . 16. (JI.:t· , ,;.J J3 ,84946 ?4!10. 27 1,67456 ,4106 0.'52 ~ . 1!> . ( 0 5,411!5 ,85732 2460.24 1,68265 ,4734 2'52!>. 1•. n~o~ 5,8'>117 ,86532 2470.50 1,69123 ,4653 25t' '>. 13, !!0(1'1 6, 3101 ,87350 2481.08 1,70034 ,4562 2<;2 '>. 1;. onc 6,9670 • 88186 7491,99 1,71006 ,4451

• 2'52'>, 1l. UCO 1,6'142 ,89044 2503.25 1. 72050 ,4342 01 5 25 . 1 0 . uuon 11, , ~50 ,811923 2514.86 1. 73175 ,4212

46 NAVAL IUEAICH LAIOIATORY

APPENDIX B

THERMODYNAMIC PROPERTIES OF SODIUM VAPOR (cont'd) (Monomer .Gas Base)

,. .,g h g 6 g c g , 111 0!1, . ~ r1 t ' '' 11),4~1:16 ,96517 2446.25 1.93300 ,3567 !• cr. . . "'"" 1 7),?J57 .97658 ?461. 66 1,97385 • 3111 1~ 0(" , • ~ l) IJfl 3)4,64 09 ,vae2o ;;'477.32 2,03965 ,2641 1'12'>. "j,5"'2 5 24,b25\l ,1:17662 ~310.88 1,76579 ,6374 1112~. C. • L' ' lf.l J2,6494 .89981 ~362.73 1, 79875 ,5806 1112'>, 1. f) I (, , 611,7£4 8 ,94702 2427.011 1,88235 ,4223 11'2">. • Ill' un tl6,dJ1 8 ,<;5723 ~440,91 1,90676 ,3839 1"2 0: . . H a n 117 •• .)'j8 ,96765 24i5.00 1,9.1685 ,3439 1 '! 2·· . • " ru ,, 17/,.0 / 91 ,97826 24~9.J3 1,97722 ,3024 1" 2" . • 2 u 3)8,ot35 ,98905 24 83.87 2,04253 ,2597 1P5 r , ;. • 1' ,16<' 22,5~ 0 1 .87394 2332.70 1,75885 ,6315 1"') ~ . ;. • 0~ n JJ,2406 • 90619 2376.90 1,80492 ,5535 1 P'5 . 1 • u~ 69,/4J1 ,95065 2437 , 41 1,88684 ,4044 11'5 1•, • F. r. u n 81!, 1) 533 ,96019 ?45r.32 1,91086 ,3691 111';!'. • 611 ~ 1111,5924 ,96990 2463 . 45 1,94053 ,3325 111r; r , ,4 C!J ~ 179,/ 014 ,97979 ?476.79 1,98047 ,2946 1 8 5 ,,. ,. ll 363, uii H .98982 ?490.31 2 , 04533 ,25" 1'17 5 , 1 . l l ~'i 20,01) 003 ,87130 ?334.57 1, 75213 ,6252 1'175. ~, ar,o" 21,'!1483 .87577 11340,70 1. 75811 ,6177 1117 5 , ;;o, o r. o~ JJ,!l191! • 91211 2390,42 1,81075 • 52!12 11!7'>. l . 011 n 70,7442 ,95397 2447.31 1,89111 ,3883 1'!75, , II O'l 89,2:)69 ,96289 2459,38 1.91476 ,3558 1!!7i, ,6 1. ~ 12U,1J05 ,9 7196 2471.64 1,94406 ,3223 1 8 7'i , ,4 iOn 181,9 U45 • 98118 2484 ,0 7 1,91!360 ,2877 1'l7 o; , ' 2 r 11 1 361,~157 ,99053 2496.66 2,04806 ,2522 1<l 0 1) , J ,4 '>o'\ 18,1:!251 ,86868 ?336,50 1.74560 ,6187 19 •) ~ . 3, 0 u <!2, 0:)62 ,88282 :!355,85 1. 76457 ,5944 19 0• • 2 , •Jr o J4,JI!/4 ,91759 2403.32 1, 81624 ,5046 19 0 . 1, IJ(• !J /1, 74!96 ,95701 2456.84 1,89!)17 ,3738 19 0•) . , I! un 90 ,4442 ,96536 2468.12 1,9U48 ,3439 19 1)1} , • !'l c•u n 121.6:)18 ,97384 2479 .58 1,94744 .3131 19 0'1 . . ' 0 11 1!!4, \J 'i UJ ,9'1245 2491.16 1,98663 ,2814 19 1)1} , • 2 ~ I) 311,4493 • 99117 25 02.92 2,05073 ,2490 1<l~ ~. 3. !1 ~ ? 7 11, 2J/S .86609 ?33S.49 1. 73927 • 6120 19~ 5 . 3. •J 0 J ., 22.-'? 79 • tl8947 2370,42 1,77011 ,5714 19:!">, 2 . ol') u .54,\144 . 9?.267 ~415.61> 1.82145 ,4128 19 2.,, 1. 0 r. 0 7;t,I UO e ,95980 2466.01 1,899 04 ,3606 19 2 '5 , , ~ r. 91,6 167 ,96762 2471>,58 1,92205 ,3332 1<l 2;; , , 6 110 ~ 12J.1)/9 .975 56 2487,30 1,95070 ,3049 1'l2 '> , • 4 o ~ H6,<lb 05 ,98361 2498.14 1. 98957 ~ ,2758 1<l2'5, • <! rt U 3/,,b i) /O ,99176 2509.11 2. 05334 ,2462 195 11 , 4,1 79t 1!1.8152 ,!!6352 2340.52 1,73313 ,6052 19'i U, 4. ,"J u 16, oU 97 ,86803 2J46.67 1,73896 ,6000 195 0 , 3. 1) ·: 0 22, 1' ??.9 .d957J 2384,43 1. 77655 ,5489 l.9'i r , ;. , I). 01 J,,49U 3 ,92737 '" 27,4 8 1. 82638 ,4627 1<l '> . 1. •J'J 7J,6:l8\l ,;16236 24 14.88 1,\l0273 ,3488 19 '> r· , , 6 •'U ~ 92, "/158 .96970 ;>484, 79 1,92547 ,3235 19 :) 0 , • 6 ! • 0~ 124,6500 • 97714 ;>494,82 1,95384 ,2974 195 P , • 41)0 168,4166 • 98467 25 04 , 98 1,99242 ,2708 19? 11 , . 2 0 0~ 379,7~0 2 .99229 2515 . 24 2,05590 .2436 1?7 4,5 P 14,5JI5 ,86096 2342.60 1,72716 ,5982 197 ':\ , 4, (JIJO 16,91.54 ,87482 2361.H 1. 74506 ,5816 19 7 . • 3, 01)\l 2J ., ~413 ,90160 23<:>7,88 1. 78211 ,5274 19 75, ~. :) n 1 J6. 0.!69 • 93172 2438,81 1.83105 ,4442 19 71;; , 1. CJ110 74,6 051 .96471 241!3,46 1,90621 ,33111 197'>, • b 0 1 9J,9226 • 97161 24?2. 7b 1,92877 ,3147 197.,, .11 1' 01} 1?.6,1297 ,97859 2502.18 1,95687 ,2901 1975, ,4 ~UIJ 190,5'i9t! ,98565 ?.511. 69 1. 99519 ,2663 1975 , .1. 00 J't3. 811 0 3 .99279 2521.30 2. 05140 ,2413 2no c. , 5, CCo 97 lJ. 3815 ,85842 2344.73 1.72137 ,5912 •

- - -- ---ii'.it'"> . 2:; 2'>, 2'i 2"> , ~'i2 5 ,

:<:<;<! "> . 2'52"> . 2'i2'>. 2'i2 . • 2')?'i, c'i2'>. 2'>?!>. 252?. 2?2 ':> . ~55 ~ . 0/'i<; O, '- o; s r . 2'iS I ,

~o:;:, r • t 55 1 • ~o;; • 2?5 j!'i'i (t . 2'i<; 2<; 5 2 '55 2?'::' C!'i~ n .

<;'i':' l . 2S5 r , 2? 5 •: . 2'i5 1l , 4''i5 1J . 2'i? lt . 2">5 0 . 2'i 5 0 . 2'!i5 11 , 2'55 • 2'15 0 , 2'15 0 , 2'!i5 l . 2">!> 0 , 2 'i5 2'i 'l:O . 257!> , 2'i7~.

2'i 7~ .

25 7'i . 2';75 . 25 75 , 2575 , 2'i75, 2'575, 2575, 2575 , 2'iH, 25 7 !> . 25 75 , 2'i75, 25 75. 25 7'>, 257 • 2'5 7!> , 2'i75, 2575, <!'i75, 2'57 'i , 2'575, 2575, 257'5, 2'57'5o 2'575, 2'575,


APPENDIX B

THERMODYNAMIC PROPERTIES OF SODIUM VAPOR (cont'd~ (Monomer Gas Base)

p

• r. ~ u

J • .. ' 11 r t • [o . u ; , t. . ,, n 4 • '·' r l •""' ~. u:· "'r: t- • ~ :. fi

• 4 .. C' i'

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c;... fJ nr, "\ ~ l • t) , , (J ,.,

; · , l• 1 IJ ,,

~· • .; r l. ~ 1 • "'(: 11

1 i , t; C G til ' L n ' n 1 ~ • • r ' 1'-, ljr,rr 13 . ur n

n:. " ~, 11. .1 ~ n . or ur:

so . 00 b. r r 11 r / , GCu e. '! •· ., • t l ~

~. O!'L n

.;, • . r IJ r

2. 0 1 ~

1 . ve l1'l . er ur • ~ .. c• • 4 ( ,,

.~ n o ;;>!:i . e"' 3~ ?5 . nun j? 4, Q Q0.1

<' l. ?O . o un 1Y. ll OUO 11!. 00 p, lJ 0 t6. U ll 15. 0 l Oll 1~. nr·uu 13 0 . 0 12. r o u. ~ o

10 . o r; un r;, or. ~

I<, OIJ 7, o n ~

t. or, t n ;. uc o ~. ooon

·'- or on ". !'on 1. or.• u

,!l lj(J II .r- r o .• un 0 ~ nc·

9 0')1)/3 1 0 o~ I .S O 12 .::- :o:o o l4 0 t! U 1~

t7. 9:0 0 \1 2coo t10~ jiJo!'>/1 0 Cb,3 bl8 9..So / '> 4 t

117,4:>..12 1~6.11 '>211

2J:>o11 :0 4t 472.~615

.lo C\167 lo . 6 .1 9 ..1,3 .!3 ,s,,l:!2 J 0 7 ~ U .1, 9 41~

4o t~6l

4o4:> 83 40 71)2 5o lJ :>4 :>,4'ol47 ., 0 ;14 1)'1

6o4?6t 7 0 P ~IIO

loll.!l iloi\Jl~ ti 0 1'1 H43

1 1. o ,,r• <: o t4! 0 "'li t 14olll>:;l 1 tlo ~ 4 C2 ' lco9:~~ J U o !.l>~!l

<4 6 0 /';J' 'll•o:> " .SQ

118o 4 'H6 1 5do3 JcJ 2Ho9154 476oll681

2o<lc!94 .I 0 ":> /5 .So<i162 ..Sold77 3,5140 ..So71/6 4o0013 4o~<485

4o5c32 4oiiJ07 , o1171 5,5103 6,00!1)7 6,5414 lo1!>02 /,tl/13 ti,7J84 'tl .oiiU01

11,lc97 12o8418 Uo1218 111o3J2D 23,1<428 31,1670 •P,22J9 9;,4118

1111,!SJ82 1'HI,6699 2Ho9'H8 4!10,9728

.11 0826 ,111752 ,\12 70 2 .113 676 • 9 674 ,9 5696 ,96740 ,97806 .98893 ,99113 ,\1\1.!33 ,99555 . 99777 • 1;073 ,79406 ,1!0196 .80964 .81717 .1:12461 .832 03 ,(:j3945 ,!14693 .115449 ,d6216 . 86997 .87794 ,89609 .89443 .9029 7 ,91172 ,9:.!069 ,92987 • 939;!7 ,\148118 . 95871 . \16874 ,97d97 .98939 .Y91!50 ,99H2 • 99574 • 9\1786 ,78602 ,79300 .110078 • 80833 .81!571 .112299 ,83021 • 83742 o84466 • 85196 .11!5933 .116682 ,8744!5 .88222 ,8901!5 .89826 ,906!5!5 .91503 ,92370 ,932!58 • 9416!5 ,9'5091 oY6037 ,97001 o97983 ,98983 • 99185 ,9\llU 0 99!591 .9979!5

?526.82 ;;>539.15 2551.84 25t-4,!17 ;>5711. 25 2:;91 .95 26 !5.9 11 262 0.30 ;?6l4,91 <'6'7.87 2640.83 ;l643.81 2646,7<1 23d6 ', 06 23 9. 77 2398.~8 24 7.52 2416.34 ;4'?5.22 24 u. 2 0 '443, 3 2<4'i2.65 :1 4~2.1 8

2471,97 ?4'1~. 0 2 ?4~2.37

;S il 3. 02 :?5 13.98 :?5 2'L27 .r'5!6.88 ?54d,82 '561. 07 ?573.65 25116.53 :.!5 'hl 71 2613.18 :::.6?.6. 93 264 0 ,94 ?643,77 :2646,61 2649,46 ?652,32 2386,47 2H4.20 240.;!,97 2411.63 '4?.0 • .25 2428.89 ?.437.59 2446,41 245'5.38 2464,53 2473,89 24113.48 24<13.33 2503,43 2513.82 2524,49 2535.46 2546,72 2558.27 2570.12 2!582.2'5 2594,66 2607.35 2620o29 2633o 49 2646o93 2649.64 2652o37 26'5!5.10 2657.84

1o74J99 1,7'5741 1, 77230 1o78908 1o80840 1. 83135 1,8'5996 1o8988'5 1o96268 1o98275 2o00841 2o04424 2o10494 1o62112 1o62552 1o63141 1o63744 1,64364 1o6!50 05 1o65671 1o66365 1,67091 1,67853 1,68657 1.69507 1o70410 1,71374 1o 72408 1,73523 1o7473!5 1o76064 1, 77538 1o79201 1o81116 1o 8J393 1o 86237 1o90106 1o96469 1,98472 2o01034 2 o 04U3 2,10678 1,61932 1. 62418 1,62988 1,63570 1,6416!5 1,64779 1, ' ,41'5 1, c 607!5 1,66763 1o67484 1o68240 1o69038 1o69881 1' 70777 1. 71732 1o727!56 1o73860 1o7'5060 1o76376 1. 77838 1. 7948!5 1o 81311!5 1 ,8J646 1,86472 1,90323 1,96667 1,98667 2.01224 2o04100 2 o10161

o4067 o3908 • 373'5 o3'547 .3346 • 3131 o2904 o2666 o24111 .2367 o2316 o2264 o2212 o53112 o!5330 o!5220 o5130 .!50'54 o4986 o4922 ,4859 o479'5 ,472'5 o4649 ,456!5 ,4471 ,4366 o4249 ,4120 o3978 o3823 o36!55 0 3474 oJ282 o3078 o21163 o2637 o2403 o23'55 o2307 o22'58 o2209 o'5475 o!53'50 o'5232 o!5135 o'50!53 o4980 o4913 o4148 o4783 o471!5 o4643 o4!564 0 4477 o4381 o4275 0 4159 o4031 0 3192 .3741 ,3!579 • 3406 o3222 o3028 o2124 o2611 o2389 o2344 o2298 0 22'53 o2206

47

APPENDIX C

THE MOLECULAR COMPOSITION OF SATURATED SODIUM VAPOR AND ENTHALPIES OF VAPORIZATION

', ('2>. r»j. (*„). AA., AA.

1600. .9100 .1V39UU .003021 25.5220 1692,35 ; L833.74 1625. 1.0327 .198008 .003493 25.5904 1665 54 J 1630.27 1650. 1.1*82 .2Ü20J9 .004U23 26.6593 1676 79 3 1626.63 1675. l.il76 .205989 .004615 25.7266 1672 09 3 1823.44 1700. 1.4P18 .209856 .005274 25.7989 1665 44 3 L820.10 1725. 1.6*20 .213M6 .006005 25.8697 1656 66 3 1816.82 1750. 1.^90 .21732/ .006813 25.9412 1652 34 1813.60 1775. 2.0740 .220924 .007702 26.0136 1645 67 J 1810.44 1S00. 2.3081 .224427 .008679 26.0669 1639 47 3 L807.33 1825. 2.5*25 .227SJ0 .009747 26.1612 1633 12 ! 1804.29 1*50. 2.838? .2illJ3 .010913 26.2366 1626 63 ; 1601.32 1875. 3.1365 .2343.11 .012181 26.3132 1620 59 ; 1798.40 1900. 3.4b86 .2J7«t22 .013555 26.3910 1614 40 : 1795.53 1925. 3.8n57 .2404UJ .015U40 26.4701 1606 24 : 1792.72 1950. 4.:7Vt .2432/1 .016641 26.5507 1602 12 : 1789.95 1975. 4.5H0n .246024 .018361 26.6327 1596 03 J 1787.23 2000. 5.un97 .248660 .020205 26.7163 1589 95 : 1784.53 2025. 5.4^94 .2511/5 .022176 26.8015 1583 86 3 1781.67 2050. 5.9ft0ft .253568 .024277 26.8684 1577 60 3 1779.21 2075. 6.4M5 .255838 .026510 26.9770 1571 72 3 L776.57 2100. 7.0424 .257981 .026878 27.0675 1565 61 3 L773.92 2125. 7.6356 .259997 .031363 27.1598 1559 46 3 1771.24 2150. 8.2*5* .261684 .034025 27.2540 1553 26 3 1768.54 2175. 8.9335 .263641 .036806 27.3501 1546 99 3 1765.79 2200. 9.6408 .265267 .039725 27.4481 1540 65 3 1762.96 2225. 10.3*88 .266763 .042763 27.5482 1534 20 3 L760.09 2250. 11.1789 .26812/ .045978 27.6501 1527 64 3 1757.10 2275. 12.0122 .269360 .049309 27.7541 1520 95 3 1754.00 2300. 12.8903 .2/0462 .052774 27.8601 1514 10 3 L750.76 2325. 1.3.8143 .2/1435 .056370 27.9679 1507 09 3 1747.36 2350. 14. /»56 .2/22/9 .060094 28.0778 1499 68 3 1743,76 2375. 15.8055 .2/2995 .063943 28.1695 1492 45 3 1739.99 2400. 16.875? .273586 .067912 28.3030 1484 78 3 1735.96 2425. 17.9961 .2/4053 .071997 28.4184 1476 84 3 1731.68 2450. 19.1*93 .2/4399 .076193 28.5355 1466 61 3 1727.09 2475. 20.396? .2/462/ .080496 28.6543 1460 03 3 1722.16 2500. 21.6779 .2/4739 .084898 28.7748 1451 09 3 1716.89 2525. 23.0156 .2/47,18 .089395 28.8967 1441 74 3 1711.19 255n. 24.4:05 .27462/ .093980 29.0202 1431 93 3 L705.02 2575. 25.0*38 .2/4411 .098647 29.1450 1421 62 3 1696.34

48

■

APPENDIX D

MOLECULAR COMPOSITION OF SODIUM VAPOR

t V '2 '4 "a

nou. .91 un .iv3»ao .003021 25.5220 1600, .HnüO .l/*4Vi .002178 25.2602 l^O'i. .«■100 .141460 .00102« 24.7602 1 A 0 0 . . < '■ 0 0 .IU1271 .000344 24.2226 1*00. .2nurt .0*4702 .000049 23.6372 1*2*. 1.0527 .198008 .003493 29.5904 1^. l.&nun .1VJÖ2J .003222 25.9209 1^25, .8001 .164103 .001822 29.0621 l^i*». . * " ü n .130910 .000853 24.6169 1*25. . 4 n ü n .U9321/ .000283 24.1191 1A2^. .2(0'' .0*0038 .000040 23.9609 1*50. l.l*d3 .202039 .10*023 29.6593 1**0. 1.0 "0-1 .1606/2 .002719 25.3296 1*50. .8(100 .1S2604 .001527 24.9196 1*511. .*rQri .121207 .000710 24.4666 1*50. .♦PQT .085883 .000233 24.0257 1*50. .2001 .045841 .000033 23.9297 1675. 1.J17* .«(05989 .C04615 25.7286 1*75. l.COOO .1686/1 .002296 29,1945 l«7'i. .hron .14194/ .001281 24.7717 1*7S. .ICU" .112286 .000591 24.3686 \>>T>. .«' 00 .0/9205 .000193 23.9414 1*7'3. . 2 r o o .04^059 .000027 23.4641 1700. l.4«l»( .209856 .005274 29.7989 1700. i. o (i o o .157484 .001942 24.9943 1700. . 8110 0 .132083 .001077 24.6366 1700. .6" 0" .10409/ ,000494 24.2616 1700. .4(100 .0/3123 .000160 23.8692 1700. .2000 .038648 .000022 23.4432 17?5. 1.662" .213636 ,006009 29,8697 1725. I.0000 .14/0/1 ,001649 24,8476 1725. . P n u n .122962 .000907 24,9136 1725. .ftUO" .0965/5 .000414 24.1641 1725. .41100 .067582 ,000133 23,7963 1725. .ifOO .035568 .000018 23.4064 1750. LP^flO ,21732/ ,006813 29.9412 1750. l.üroo .13/391 ,001399 24,7134 17*0. .8000 .114532 ,000766 24.1012 1750. .61 ü: .089669 .000347 24.0755 1750. . 4 n o n .062531 ,000111 23.7338 1751'. .2000 ,032/82 .000019 23.3732 1775. 2. J74n ...•20924 .007702 26.0136 1775. 2.0^00 .215620 .007090 25.9215 1775. I.onoo .12839V ,001186 24,5904 1775. ,8000 .106/4/ ,000648 24.2985 1775. .6000 .083329 ,000292 23.9946 1775. .4roo .057924 .000093 23.6772 1775. . .10 0 0 .030260 .000013 23,3432 1«00. ?.im .22442/ .008679 26.0869 IflO". 2.unün .203/53 .006114 29.7290 1500. i.onoo .120052 .001010 24,4/76 noo. .81-00 .099558 .000549 24,2046

49


APPENDIX D

MOLECULAR COMPOSITION OF SODIUM VAPOR (cont'd.)

t P *3 x* "a

IflOO, .a; u" .U/7sU/ .L00247 23.9?13 i«ou. .*' uo .II5.J71V .UOQO/fl 23.6258 l«00. .2000 .U27V/4 .000010 23.3161 Ifl35. i.?»-?? .227ijja .C09747 26.1612 l^Z1». «r.Jû" .1V25U9 .C05305 25.55CP l^ZS. 1. 0' u o .112310 .000661 24.3743 \^2^. .»■. Ü0 tWtiVHu .000467 24.1188 I***. .«nop .0/2160 .000209 23.8642 IflZi. . 4 " U 0 .0490/^ .00Ü066 23.5790 l«2i. ,2i 00 .0^5898 .003009 2?.2916 l«5ü. 2.83«? .2J11J3 .010913 26.2366 1R50. i.J|i0■, .löld/b .004607 25.3861 IMP. l. o r o o .105150 .C0Q736 24.2795 IfJ'i. . d u i .186/V.5 .C0U397 24.0402 l<»5r;. .i'Ü'1 .067246 .000177 23.7930 issr1. . «'■ 0 ' .04636/ .000056 23.5364 I85n, .i'|,oo .024010 .000007 23.2693 IR?^. 3.1565 .^34.5,51 .012181 26.3132 l«»?^. 3.') i ü 0 .^2//84 .010956 26.1975 1«73. 2.Jf00 .i/lbJJ .004005 25.2336 1«7>5. 1,0000 .0964/3 .000631 24.1924 1K7S. .«roo .081134 .000339 23.9682 !«;->. .«r o n .062/29 .000151 23.7370 1^79. .«''oo .043155 .000047 23.4976 l«75. . 2 f o n .022292 .000006 23.2490 140:. 3.419^ .237422 .0)3555 26.3910 190". 3.0i;uo .21669/ .009647 25.9943 loon. z.ncoo .162364 .003495 25.0924 1900. i.nouo .092301 .000541 24.1124 1900. .«ôo .0/5908 .000290 23.9022 1900. , ft o o n .0585/4 .000124 23.6859 1900. .«'■'JO .040212 ,000040 23.4622 1900, .2^0 .020726 .000005 23.2306 192^). 3.«■'57 .240403 .015040 26,4/01 192^). 3.ünuo ,206103 .008498 25.8146 1925. 2.üru0 .15344'j .C03037 24.9619 1925. i.ot'ün .0865/8 .000465 24.QJ88 1925. .<Jr0O .1/10 8 0 .000249 23.8416 19?5. .soon .054749 .000110 23,6389 192«!, .« )U0 .037514 .000034 23.4299 1925. .2rQ0 .019295 .000004 23.2139 1950. 4.1791 .2432/1 .016641 26.5507 1950. 4.ill 00 .<36865 .015023 26.4160 1951. 3. (j 0 0 0 .195999 .00/490 25,6473 1950. 2.0000 .14SÜ92 .002649 24.8409 1950. l. u p o n .0812/1 .000401 23,9711 1950. .8000 .06661/ .000214 23.7959 1950. .ftOdO .051226 .UOÜ094 23.5959 1950. .4100 .035038 .000029 23.4003 1950. .2100 .0179S2 .000004 23,1985 1975. «.SHOO .246024 .018361 26.6327 1975. 4,onon .22638/ .013368 26.2207 1975. 3.orü0 .1863/9 ,006607 25.4917 1975. 2.0100 .137160 .002314 24.7286 1975. 1.0000 .0/6349 .000347 23,9087 1975. .eôo .062491 ,000184 23.7347 1975, .6000 .04/9/9 .000081 23.5563 1975. .4000 .032763 .000025 23,3731 1975. .2000 .016/91 .003003 23,1845 2000. 5.0197 .248660 .023205 26,7163

■. t .»■-


APPENDIX D


t P X2 '« "a

2nf". 5 . ü r 01 .<i4ft3Ha .020116 2f.7099 ^OOP. 4. o n ü i .216310 .011899 26.0383 2100. 3.uföi .1772J2 .015832 25.3468 2f,ÜJ. 2 .0 ü u i .1297«3 .002024 2«.62*6 ?no", 1 . ü !' L 1 .0/17112 .r.00300 23.8512 2nor. .felÜI .0506/2 .000159 23.6675 2^00, .6101 .044982 .000070 23.5200 2P00. . « ' b 'I .U906/1 .000021 23.3482 »"OC .?.'i01 . Ü156V«! .000003 23.171/ 2C2(>. b.«K)* .2511/S .022176 26,8015 2n25. 5.0'01 .^382/9 .018043 26.5065 2D25, «. ü n ö o .205641 .010594 29.6690 2026. 3 . 0 ' ü i .168348 .005152 29.2119 2n2'5. <r . ii L ü 1 .1227// .001773 24.5282 202^. 1.0100 . 06754<i .000260 23.7981 2n2S, . Ö " U 1 .05513/ .000138 23.6441 2',2I5. .*rlJ T .04221S .000060 23.4666 2P2S. .«: 01 .028745 . 000018 23.3254 2025. .2101 .01468/ .000002 23.1599 2150. •-.«'0«. .253568 .024277 26.6864 2C50. S.OPOO .226505 .016185 26.3159 ZfSC. «.t-ioo .1*73// .009438 29.7090 2'150. S.lil'Ql .160311 .014556 25.0663 2P5D, Z. 0 ') 0 3 .116235 .001556 24.4386 2^50. i. ü r o i .0636C5 .000?26 23.7491 znsc. .bru" .051862 .010120 23.6040 2n5rl .ftPU" .03V659 .000052 23.4556 2n5r. ,4001 .026969 .0110016 23.3043 2150. .2riji .013761 .000002 23.1491 2n7!>. 6.4<'45 .25583« .026510 26.9770 2175. 6.0100 .2446/1 .022245 26.7050 2',/9. s. o c n n .2190/0 .014521 26.1374 2175. 4 . 0 T; 0 0 .186518 .006413 25.5604 2175. S.OiQi .152505 .004034 24,9693 2175. 2. 'J

n r i .110094 .01)1367 24,3655 2175, 1,, U101 .059946 .030197 23,7036 2175. .8100 ,0*8825 .000104 23.5670 2n75. . 6 '■ 01 .037295 .000045 ..3.4275 2175. .4101 .025332 .000014 23.2850 2175. ,?i'0P .012910 .000002 23,1392 ZJOO. 7.0*24 .^57981 .026876 27,0675 2111. 7.0n01 .257143 ,0?8494 27.0450 2100, ft.0101 .235506 .020062 26.5118 2100, 5.0100 .209980 .013033 25,9703 2100. 4.0101 .18005/ .007504 29.4215 2101. 3.1 n0'1 .145113 .003575 24,6602 2101. 2 . 0 '■ 01 .1043.50 .001203 24.2762 2101. i.oroi .1)56545 .000172 23,6616 2101. .Bi-iOO .046008 .000091 23.532/ 2101. ,6101 .035106 .000039 23,4013 2101. ,4001 .023819 .000012 23.2671 2100. .2101 .012125 .000002 23,1301 212''. 7.^i5ft .25999/ .031363 27,1598 2125. 7.ü■^0', .247992 .025865 26.6383 212'i. 6.010" .226426 .018131 26.3285 2125. 5.0101 .201239 .011701 25.6137 212S. 4.0001 .1/1984 .006699 25.2916 2125. 3, o r o o .13811/ .003172 24.7985 212^. 2. 0 0 Ü 0 .098919 .001060 24.2063 2125. 1.0101 .053381 .000151 23.6230


APPENDIX D


t V *2 '« «a

US*. .«"03 .Ü43.JVJ .J00079 23.9011 ül?^. .6" UP .03iÜ/8 .DOÜ034 23.3770 iu*. . «'• 0 0 ,022420 .030010 23.2506 ütS«-. .2rün ,011401 .000001 23.1216 2150. 8.266« ,261bH4 .034025 27,2540 2isn, 6. 0 0 U1 .25746/ .031681 27.1264 235:. V. 0 r 0' .23V06/ .033475 26,6437 215' . 6. Ü C Ü 0 .2176J« .016372 2ft.1574 2150. b.Oi-Ol .1^2845 .010511 25.66/0 2150. 4 , U11 0 0 .164291 .005985 25.17P4 21 5r. 3. con .1315UÜ .002818 24.6635 2150. 2.0000 .U9J84U .000936 24.1394 215". 1.000« .Ü504J6 .000132 23.5d7o 2150. . 8 - ij n .040962 .000069 23.4718 2150. .ft-. 0 0 .U311V/ .000030 23.3546 2150. .4ron .021125 .000009 23.2354 2150. .?'0o .0X07.52 .000001 23.113« 2*75. 8.9XJ5 .263641 ,ui6806 27.3501 2175. b. 0 0 0 0 .2«B78^ .028890 26.9220 2i 75. 7. con .2^0383 .021306 26.4607 2175. ft . c r 0 o .209153 .014788 25.9968 2175. b. 0 0 Q o .184/V6 .009447 25.5296 217S. 4,0000 .156966 .0 05352 25.0669 2175. 3.0001 .125242 .002506 24,5749 21 75. i. 0 0 0 0 . Ü H 9 Ü / 2 .000828 24,0770 2175. 1. 0 0 0 0 .047693 .000116 23.5535 21 75. .9flC0 .038703 .000061 23.4446 2175. .SOQO .029451 .000026 23.3339 2175. .4C0n .019925 .000008 23.2213 2175. .2000 .010113 .000001 23.1067 2?0G. V.6<üH .265267 .039725 27.4481 2200. 9.0 r 0 0 .256221 .034246 27.1681 2?00. 8.0000 .2402VQ .026340 26.7292 2?0o. 7,0000 .221952 .019340 26.2885 2700. ft.con .2009/1 .013362 25.8460 2PU1'. 5. 0 0 0 0 .l/7üt/ .308497 25.4007 2?0P. *. u n u n .14999/ .004 90 24.9507 220C1. s.oom .119328 .002232 24.4921 220". i.uoon .084595 .000733 24.0190 2200. 1.0000 .045136 .000102 23.5226 290O, .8000 .036600 .000054 23.4193 2?0U. .ftf.on .027829 .000023 23,3146 2?Q0. . 4 r ij 0 .018812 .000007 23.2082 220O. ,2ruo .009540 .000001 23.1000 2?25. icJ^en .266/63 .042/83 27.5482 2?25. iu.or 00 .2618/5 .039453 27.3860 2225. 9. U10 ft .2479/4 .031351 26.9675 2225. 8.0OUO .2.1200/ .024015 26,5476 2225. 7.0000 .213782 .01/558 26,1266 2225. 6. u 0 u n .19.5094 .012080 25.7044 2225. i.ocun .169712 .00/648 25.2800 2225. 4,13000 .143369 .004292 24.8512 2225. 3.0000 .1137,5/ .001990 24,4147 2225. i. 0 0 01 .080391 .000651 23,9648 2225. 1. D 0 o 0 .042750 .000090 23.4936 2225. .8100 .034641 .000047 23,3959 2225. .6000 .026320 .000020 23,2967 2?25. .4000 .0177/9 .000006 23.1961 2225. .2000 .009009 .000001 23.0938 2250. 11.1/89 .26812/ .015978 27.6501

■


APPENDIX D


t P I '« ".

2»50. u.ocnn .26A118 .044452 27.5/89 225P. lO.ooon .2b3bV9 .036252 27.1792 2?5n. 9.Q0UT .2398V5 .026697 26.7761 2?5n. e,oron .22394!) .021896 26.3764 2250. 7.0000 .205860 .015946 25.9742 2?50. 6.0000 .165520 .010926 25.5713 2250. b.onoo .162661 ,006869 25.1666 2250. 4.0000 .1370/0 .003890 24.7561 2251. 3,oneo .108455 ,001777 24,3423 2250. 2.0000 .0/6441 .000570 23,9142 2250. l,unon .040524 .000060 23,4667 2250. ,0000 .032615 .000042 23,3740 2250. ,6000 .024916 .000018 23..-'801 2250, . 41 0 0 .016619 .000005 23,1849 2250. .2^00 .006516 .000001 23,0861 2275. 12.0122 .269360 .049309 27.7941 2275. 12.0000 .26923/ .049206 27.7495 2275. 11.0000 .256424 .040962 27.3671 227S. 10. 0 n o 0 .246056 .033303 26.9635 2275. 9.ÜD0O .232001 .026267 26.5993 2275. e.uooo .216114 .019967 26.2151 2275, V.onoo .198246 .014487 25.8309 2275. 6.U0U0 .1/8246 .009868 25.4464 2275. S.onon .19592/ .006210 25.0603 2275. 4.U0OO .131085 .003457 24.6707 2275. 3.00OO .103462 .001589 24.2745 2275. 2.0000 .072729 .000515 23.8669 2275. 1.0000 .038444 .000071 23.4416 2275, .0000 .031112 .000037 23.3937 2275. .6000 .023607 .000016 23.2647 2275. .4roo .0^5925 .000005 23.1744 2275, ,2noo .008056 .000001 23.0628 2300. 12,6903 .2/0462 .052774 27.8601 230n. 12.0000 .261626 .045503 27.5340 2300. ll.onoo .250635 .03/771 27.1665 2300. 10.0000 .23836/ .030589 26.7989 2300. 9.0000 .224,303 .024043 26.4306 2300. B.oroo .2U8520 .016213 26.0631 2300. 7.oroo .19066(1 .013167 25.6961 2300. 6.0C0O .1/1266 .006955 25.3289 2300. 5 . 0 f 0 0 .149499 .005604 24.9605 2300. 4.0000 .125401 .003107 24.5866 2300. 3.0000 .096745 .001423 24.2110 2300. 2.0000 .069240 .000459 23.8227 2300. 1. 0 c o o .U365ÜÜ .000063 23.4183 2300. .8000 .029521 .000033 23,3346 2300. .6000 .02238/ .000014 23,2903 2300. .4000 .015093 .000004 23,1647 2300. .2000 .007632 .000001 23.0779 2325. 13.8143 .2/14J5 ,056370 27.9679 2325. 13.0000 .264321 .049789 27.6619 2325. 12.0000 .25449J .042062 27.3295 2325. 11.0000 .24336/ .034804 26.9766 2325. 10,0000 .230641 .026095 26,6237 2325, 9.0000 .216611 .022010 26,2714 2325, e.oooo .20116/ ,016617 25.9200 2325, 7.0000 .16379/ .011973 29,5692 2325, 6.0000 .1645/6 .008116 29.2185 2325, 5.0000 .143366 .005061 24.8667 2325, 4.0000 .120004 .002796 24.9120


APPENDIX D

MOLECULAR COMPOFITIQN OF SODIUM VAPOR (cont'd.)

t i

P '2 '. "a

2325. a.anun .U44287 .001276 24.1515 2325. i.&oun .065959 .000410 23,7814 2325. l.uouo .034682 .000056 23,3965 2325. .8000 .028035 .100029 23,3172 2325. .6000 .021248 .000012 23,2369 2325. .4000 .01431/ .000004 23,1556 2325. .2cun .007234 .000000 23,0733 2350. 14,7H6A .2/22/9 .060094 28,0778 2350. 14.0001 .266083 .053826 27,8129 2350. 13.0000 .25/244 .046149 27.4746 2350. 12,00 00 .247258 .038871 27,1356 2350. 11,0000 .236038 .032066 26.7968 235P. 10,0000 .223493 .025804 26.4585 2350. v. o o u n .209531 .020153 26.1212 235(1. a.ocno .194058 .015168 25.7850 2350. 7.0000 .1/69/3 .010894 25.4497 2350. e.ocon .15816/ .007361 25.1146 2350. 5.0000 .137518 .004?75 24.7786 2350. 4.0000 .1148/9 .002519 24.4398 2350. 3.0000 .0900/3 .001145 24.0957 2350. 2.0001 .0628/2 .000366 23.7427 2350. 1,0000 .0329/9 .000050 23.3761 2351.'. .eruO .02664b .000026 23.3007 2350. ,6001 .020184 .ooooi-. 23.2244 2351). .4001 .013593 .000OC 3 23.1472 2350. .2101 .006866 .000000 23.0690 2375. 15.8055 .2/299t .063943 28.1695 2375. 15.0000 .267246 .057617 27.9286 2375. 14.0000 .259253 .050018 27.6034 2375. i3.onoo .25024Z .042762 27.2/76 2375. 12.0001 .24013/ .035915 26.9518 2375. 11. 0 o 0 0 .^28859 .029541 26.6266 2375. i o. u c o n .216330 .023704 26.3024 2375. 9.0000 .202469 .018458 25.9795 2375. 8,0000 .187193 .013851 25.6578 2375. 7.0100 .170413 .009918 25.3372 2375. 6.0000 .152Ü-SZ .006681 25.0168 23/5. 5.0000 .131943 .004140 24.6957 2375. 4.0000 .110015 .002272 24.3720 2375. 3.0000 .086089 .001029 24.0433 2375. 2.0000 .059966 .000328 23.7064 2375. I.0000 .03-384 .000044 23.3571 2375. .8000 .025344 .300023 23.2853 2375. . 6 r> o n .019190 .000010 23.2127 2375. .4000 .012916 .000003 23.1393 2375. .2001 .006521 .000000 23.0650 2400. 16.875? .2/3586 .067912 28.3030 240". 16.0001 .267920 .061156 28.0304 2400. 15.0000 .260655 .053661 27.7177 2400. 14.0C00 .252482 .046460 27.4042 2400. 13.0000 .243334 .039614 27.0907 2400. 12.0000 .233144 .033160 26.7777 2400. 11.0000 .221843 .027217 26.4656 2400. 10.0000 .209361 .021776 26.1549 2400. 9.0001 .195628 .016911 25.8457 2400, e.oooo .1805/0 .012654 25.5379 2400. 7.U001 .164110 .009036 25.2311 240U. 6.0000 .146163 .006069 24.9248 2400. 5.0000 .126630 .003749 24.6177 2400, 4.0000 .10539/ .002052 24.3082


APPENDIX D

MOLFXULAR COMPOSITION OF SODIUM VAPOR (cont'd.)

2*00. 3.oroo 2«on. i. C o u 0 ?40n. 1.0001

240r. , ft" n f

2«on. .600"

2«00, ,4*00 2<<on. ,2i>or

2«2'>. i ;,v<i6i 242^. 17.1J('U"

242'>. 16,0000

242^. 15.fOOP

242'i. 14.0000

2425. 13.000*

2425. If.0001

2425. 11,000" 2425, 1O.CO00 2425. 9, OnQO

2425. B.ÜOQO

2425. 7.0n0P 2425. 6.CO00

2425. 5. o r ü n

2425. 4. o o o r 2425. 3 . U r 0 3

2425. 2.0000

2425. 1.0000

2425. .eôo 2425. .Arûo 2425. .4000

2425. . 2 0 C n

245n. l»,l^«l 2450. l^.OÛ"

2*50. m. o c on

2450. 17. r" 0 o 2450. 16,000" 2450. Ib.onoo

2450. 14.0000

245^. 13.000" 2450. 12.0000

2450. 11.0000

8450. 10 . 0 0 C 0

2450. 9.000^

2450. b, on on 2450. 7.0000

2450. 6. 0 0 ü n

2450. 5.proo

245ri. 4.or O"

2450. 3.1000

2450. i.OtC" 2450. l.OCQO

245 . .BCO'1

245". .6000

2451. . 4;; 0 0

2450. .2000

2475. 20.396'

2475. ?c.onon

2475. 19.0000

2475. IB, fir 00

247>>. 17 . 0 r 0 ^ 2475. 16,0000 2475. 15.00 00

.002323

.05/229

.o^Vbbv

.02412«

.018259

.012284

.ÜÜ6199

.274053

.268194

.2615!)/

.284107

.245786

.236534

.226291

.214996

.202589 ,189008 .17418« .158060 .1405*9 .12156/ ,101013 .0/8/60 .054651 .028485 .022983 .01738/ .011692 ,005898 .2/4399 .2/354/ ,26813/ ,262046 .255224 .247620 .239181 .229854 .21958/ .20B326 .196019 .182610 .168043 .152256 .135182 .116745 .096851 .0/5390 ,052221 ,027168 ,021912 ,016569 ,011138 .005616 .2/462/ .2/290/ .Ü6/8U/ .262193 .235919 .246939 .241208

.000927

.000295

.000040 ,000021 .000009 .000003 .000000 .071997 .064450 .05/076 .049956 .043144 .036691 .030653 .025078 .020014 .015500 .011568 ,00823»« .005518 .003400 .001855 .000835 .000265 .000035 .000018 .000008 .000002 .000000 .076193 .074924 .067509 .060268 ,053247 .046494 .040056 .033982 .028319 .023112 .018399 .014213 .010581 .00/516 .OC5022 .003086 .001679 .000754 ,000238 .000032 .000017 .000007 .000002 .000000 .060496 .077590 .070341 ,063242 .056333 .049659 .043261

23.9941 23.6724 23.3393 23.2709 23.2018 23,1319 23.0613 28.4184 28.1198 27,8187 27.5169 27.2149 26.9134 26.6127 26.3134 26.0155 25.7194 25.4247 25.1312 24,8381 24.5443 24.2482 2^.9479 23.6405 23.3226 23.2574 23.1915 23.1250 43.0578 28.5355 28.4868 28.1980 27.9078 27,6170 27.3259 27.0351 26.7452 26.4565 26.1693 25.8838 25.6001 25.3180 25.0369 24.7563 24.4751 24.1918 23.9044 23,6105 23,3070 23,2448 23.1820 23.1186 23.0545 28.6543 28.5444 28.2659 27.9861 27.7055 27.4246 27.1442


APPENDIX D


t P X2 '♦ ".

2475 14,0000 .2326/9 .037185 26.8644 2475 iS.oroo .223305 .031473 26.5857 2475 12.0000 .213040 .026167 26.3085 2475 11.0000 .201638 .021304 26.0330 2475 lO.OTOO .189651 .016920 25,7593 2475 e.cion .176432 .013040 25,4875 2475 0.0000 .162129 .009684 25.2172 2475 7.0000 .146690 .006862 24,9480 2475 6.0000 .130053 .004574 24.6793 2475 5.0000 .112150 .002803 24,4099 2475 4.0000 .092900 .001522 24,1386 2475 3.0000 .072201 .000682 23.8635 2475 2.0000 .049930 .000215 23.5823 2475 1.Ü00C .025930 .000029 23.2923 2475 .8001 .020905 .000015 23.2329 2475 .6000 .015802 .000006 23.1730 2475 .4non .010616 .000002 23,1125 2475 .2000 .005352 .000000 23,0915 2500 21.6779 .2/4739 .084698 28,7748 2500 21.0000 .271892 .080040 28,5934 2500 20.0000 .267253 .072957 28,3246 2500 19.0000 .262056 .066005 28,0545 2500 le.oron .256261 .059219 27,7837 2500 17.0000 .249828 .052637 27,5127 2500 i6.ocon .242716 .046300 27.2418 2500 is.onoo .234884 .040247 26.9715 2500 14,0001 .226291 .034518 26.7323 2500 13.0001 .216896 .029151 26.4345 2500 12.0001 .206657 .024182 26.1683 2500 11.0000 .195535 .019644 25.9040 2500 10.0000 .18348/ .015566 25.6416 2500 9.0001 .1704/1 .011970 25.3610 2500 e.oooi .156443 ,008869 25.1220 2500 7.0001 .141355 .006271 24.8641 2500 6.0C00 .125152 .004170 24.6065 2500 5.0000 .i57774 .002550 24.3484 2500 4.0000 .089147 .001381 24.0885 250n 3.0000 .069181 .000617 23.8249 2500 2.0001 .04776/ .000194 23.5558 2500 1.0000 .024765 .000026 23.2789 2500 .6001 .019960 .000013 23.2218 2500 .6000 .015082 .000006 23,1646 2500 .4001 .010131 .000002 23.1069 2500 .2001 .005104 .000000 23.0486 2525 23.015« .274738 .089395 28.8967 2525 23,0001 .274681 .089285 28.8927 2525 22.0000 .2/0834 .082286 28.6346 2525 21.0001 .266512 .075369 28.3749 2525 20.0000 .261682 .068566 28.1140 2525 19.0000 .256339 .061909 27.8525 2525 16.0000 .25035/ .055432 27.5906 2525 17.0001 .243789 .049170 27.3289 2525. 16.0000 .236569 ,043161 27.0677 2525. 15.0001 .228660 .037440 26.8075 2525 14.0001 .22002/ .032043 26.5485 2525 13.0000 .2106-53 .027003 26.2911 2525 12.0001 .200442 .022353 26.0356 2525. 11,0001 .189418 .018120 25.7820 2525. 10.0001 .1/7524 .014326 25.5303 2525 9,0001 .164724 .010994 25.2804


APPENDIX D

MOLECULAR JOMPOSITION OF SODIUM VAPC (cont'd.)

57 (PAGf 58 BLAN»)

( P '2 '4 «.

2^. b.!)"!)'" .15ÜW/S .008129 25.0320 2S2^. 7, U C t) 1 .U624J .005735 24,7848 2?2S. ft . C " ü 1 ,120470 .003805 2«,5379 2')25. 5, L ü 01 .103606 .002322 24,2904 252%. < . ti 1C " .065583 .001254 24.0412 2S25. 3.U"0n .066322 .000559 23.7886 2S25. 2.0^0" , 0457*3 .000175 23.5309 ZSJS. l, p n t c .U2i6/J .000023 23.2655 2525. .fcnü" .0190/0 .000012 23.2113 i^i. . ft '■ Ü " .01440!» .100005 23.1567 2525. ,4roi .0096/3 .000002 23.1016 2525. .?n0" .0u4ö/Z .000000 23.0459 2551. 2«.4J(J5 ,2/462/ .093980 29.0202 255^. ?*.0^ü" .2/J26a .091164 28.9182 255-:. ?3. jrL- ,269658 .064340 28.6686 255',. ?2.ü"l" .26561/ .077588 28.4175 255:'. 21.o"ci" .26111* .070935 28.1654 255 0. 20.000" .Ü56111 .064411 27.9126 255V. IS.Onor .*5058«! .058946 27.6594 255'. 16. C n o" .*44494 .05187* 27,4064 255?. i v. a r o n .^3/814 .045923 27,1538 255^. Ift.uCC" .200 50 9 .040230 26.9021 2550. 16.oroi .*2254/ .034«29 2ft.6516 2551. K.O'.'Ü" .213095 .029747 26.4025 2551. 13.0 " 0 n ,2045*3 .o?5oie 26.1552 255;. 12.0^" ,1V4JVÖ .020668 25.9u9b 255i- . n.uro" ,lb34öb .0167*0 25.6664 2,55'J. 1 L . C1 r L " ,1/1762 .013194 25.4249

255". s.ooc: ,1591«/ .010104 25.1852 255*. 8. 0 " o c ,1457*0 .007455 24,9470 255 0. '/ . 0 " l " .101346 .005249 24.7098 255". 6.000" ,115998 .003475 24.4730 255^. 5.0 ? 01 ,099635 .002116 24.2356 2551. ♦.Ü0Ü" ,08*197 .001141 23.9966 2550. S.OrOi .063614 .000507 23.7544 255". 2.0"0" .04379/ .000159 23.5074 255'). i.ocon .0226J8 .000021 23.2534 2550. .8"30 ,018233 .000011 23.2016 255?. .ftro" ,013 769 .000005 23,1492 255". . < C 0 " ,309243 .000001 23.0966 255". .2000 .004654 .000000 23.0434 2575. 2b.fl'3<' ,2/4411 .098647 29.1450 2575. ?5.ü"f)'-1 .2/1780 .092868 28.9377 2575, 2<.Dton .*683«/ .066215 28.6962 2575. ?3.:oc" ,264595 .079625 28.4533 2575. 22.0O0" .2603// ,073122 28,2094 257b. 21.1/001 .*55706 .066733 27,9646 2^75. ? 0 . 0 r 0 " .250553 ,060485 27.7199 2575. 1«. J'-O" .244890 .054408 27.4751 2575. 1 J>. 0 0 0 o .23^68/ .048530 27.2307 2575. 17.000" .231915 .012883 26.9871 257^. T6.C"00 ,224546 .037497 26.7446 2575. l&.COn .216550 .032400 26.5035 2575. 14 . 0 f 0 " .20/901 .C?7620 26.2643 2575. iS.ü'iOO .198568 .023185 26.0264 257^. 12.0001 .1885*6 .019117 25.7907 2574. 11, 0 f. 0 " .1/7745 .015436 25.5570 257-5. lO.Of0" .166196 .012157 25.3252 ?«;■ . v.rro" .153656 .009292 25.0952 2575. 8. u r o i .14068/ .006843 24.8f.66 2575. /.COO" .126656 .004808 24.6390 2575. 6.000" .111/26 .003178 24.4117 2575. 6.000? .J95852 .001931 24.1839 2575. 4 . n n 0 1 .0/8960 .001039 23.9544 2575. 3.0"0" .061047 .000461 23.7221 2575. 2.000" .0419/4 .000144 23.4652 2575. 1.0505 .021665 .000019 23.24:9 2575. .SCO! .31744^ .000010 23,1923 2575. . ft o C " .0131/0 .000004 23.1423 2575. .«"01 .008M08 .000001 23.0919 2575. .200" .004448 ,300000 23.0410

f

Security Classification

DOCUMENT CONTROL DATA R&D (Stcunlv clmmmllicmllon of rill*, body ol abalract and indatint mnnolalion mutt be anfarad whan Ihr ovara// report ia cla filled)

t ORIGINATING ACTIVITY rCorporata author;

U.S. Naval Research Laboratory Washington, D.C. 20390

2a RCPOBT SFCURITv CLASSIFICATION

Unclassified 2b OROi.P

3 HtPORT TITLE

High-Temperature Properties of Sodium

4 DESCRIPTIVE NOTES (Type ol report and Incluuve dalem)

A final report on one phase of the problem S AUTHORfi) (L»el name. Ural name, initial)

Stone, J.P., Ewing, CT., Spann, J.R., Steinkuller, E.W., Williams, D.D., and Miller, R.R.

6 REPORT DATE

September 24, 1965 7a TOTALNO OF PACES

63 7b NO OF REF9

29 Sa CONTRACT OR GRANT NO

NASA C-76320 b PROJEC T NO

NRL Problem C05-15

9a ORISIN'TOR'S REPORT NUMBERS;

NRL Report 6241

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10 A VAIL ABILITY/LIMITATION NOTICES

Unlimited availability. Available at CFSTI - $3.00

11 SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

NASA

13 ABSTRACT

An experimental program is in progress at this Laboratory to measure various thermophysical properties of sodium, potassium, and cesium. A final reporting of the experimental results for sodium (saturation and superheat properties of the vapor, density and specific heat of the liquid) is presented together with a thermodynamic treatment of the data. Two equations of state are advanced, one virial and one quasi-chemical; and additional saturation and superheat properties of the vapor are derived from these equations. Either of two paths can be used to compute thermodynamic properties, the monomeric gas path or the liquid path; but results obtained by the former procedure are believed to be more accurate. Enthalpy, entropy, specific volume, specific heat, and compositional information (weight fraction of dimer, weight fraction of tetramer, and average molecular weight) are tabulated for some 700 selected vapor states in the temperature range from 1625° to 2575*F and in the pressure range from 0.2 to 25 atm.

DD F^A 1473 59 Security Classification

Security Classification 14

KEY WORDS LINK A LINK B LINK C

Sodium Thermophysical properties Compressibility data Saturated vapor Superheated vapor High-temperature properties Monomeric gas path Liquid path Viri'al equation of state Quasi-chemical equation of state Thermodynamic properties Association Liquid metals

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60 Security Classification

re Properties of Sodium - DTIC · The nine PVT experiments for sodium (Table 2) covered a wide...

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